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Bài tập 83 trang 99 SGK Toán 9 Tập 2

Giải bài 83 tr 99 sách GK Toán 9 Tập 2

a) Vẽ hình 62 (tạo bởi các cung tròn) với HI = 10cm và HO = 2cm. Nêu cách vẽ.

Hình 62 bài 83 trang 99 SGK Toán lớp 9 Tập 2

b) Tính diện tích hình HOABINH (miền gạch sọc)

c) Chứng tỏ rằng hình tròn đường kính NA có cùng diện tích với hình HOABINH đó.

ADSENSE

Hướng dẫn giải chi tiết bài 83

Với bài 83, chúng ta sẽ tìm hiểu xem cách vẽ hình đã cho như thế nào và tính toán các giá trị đại số bằng công thức đã học.

Câu a:

Vẽ nửa đường tròn đường kính \(\small HI = 10 cm\)

Trên đường kính HI lấy điểm O và điểm B sao cho \(\small HO = BI = 2cm\)

Vẽ hai nửa đường tròn đường kính HO, BI nằm cùng phía với đường tròn (M).

Vẽ nửa đường tròn đường kính OB nằm khác phía đối với đường tròn đường kính HI.

A là điểm chính giữa cung OB, N là điểm chính giữa cung HI

Chúng ta có hình vẽ như đề bài

Câu b:

Diện tích hình HOABINH là:

\(\small S=\frac{1}{2}\pi. 5^2-2.\frac{1}{2}.1^2.\pi+\frac{1}{2}\pi. 3^2=16\pi(cm^2)\)

Câu c:

Ta có độ dài NA là:

\(\small NA=\frac{HI}{2}+\frac{OB}{2}=8(cm)\)

Diện tích hình tròn đường kính NA là:

\(\small S=\left (\frac{8}{2} \right )^2.\pi=16\pi(cm^2)\)

Bài toán được giải quyết!

-- Mod Toán 9 HỌC247

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  • Nguyễn Minh Hải

    Bài 65 (Sách bài tập - tập 2 - trang 111)

    Tính diện tích hình tròn biết chu vi của nó là C ?

     

     

     

    Theo dõi (0) 1 Trả lời
  • bach dang

    a) Vẽ lại hình tạo bởi các cung tròn xuất phát từ đỉnh C của tam giác đều ABC cạnh 1 cm. Nêu cách vẽ.

    b) Tính diện tích miền gạch sọc.

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<clippath id=\"clip3\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_9\"><path> <clippath> <g clip-path=\"url(#clip3)\" id=\"svg_10\"> <g fill=\"none\" id=\"svg_11\" stroke=\"#000000\" stroke-linecap=\"round\" stroke-linejoin=\"round\"> <path d=\"m198.78,196.89c0.16,20.01 10.98,38.41 28.38,48.27c17.41,9.87 38.76,9.7 56,-0.44\" id=\"svg_12\"><path> <title><title> <desc>Cung c: CungTròn[A, C, D]<desc> <g> <!-- drawing style --> <g> <!-- clip3 --> <clippath id=\"clip4\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_13\"><path> <clippath> <g clip-path=\"url(#clip4)\" id=\"svg_14\"> <g fill=\"none\" id=\"svg_15\" stroke=\"#000000\" stroke-linecap=\"round\" stroke-linejoin=\"round\"> <path d=\"m283.16,244.72c34.5,-20.28 55.55,-57.43 55.23,-97.44c-0.31,-40.01 -21.96,-76.818 -56.77,-96.55\" id=\"svg_16\"><path> <title><title> <desc>Cung d: CungTròn[B, D, E]<desc> <g> <!-- drawing style --> <g> <!-- clip4 --> <clippath id=\"clip5\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_17\"><path> <clippath> <g clip-path=\"url(#clip5)\" id=\"svg_18\"> <g fill=\"none\" id=\"svg_19\" stroke=\"#000000\" stroke-linecap=\"round\" stroke-linejoin=\"round\"> <path d=\"m281.62,50.73c-52.21,-29.598 -116.26,-29.09 -168,1.333c-51.738,30.423 -83.319,86.137 -82.842,146.157\" id=\"svg_20\"><path> <title><title> <desc>Cung e: CungTròn[C, E, F]<desc> <g> <!-- drawing style --> <g> <!-- clip5 --> <clippath id=\"clip6\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_21\"><path> <clippath> <g clip-path=\"url(#clip6)\" id=\"svg_22\"> <g fill=\"none\" id=\"svg_23\" stroke=\"#993300\" stroke-linecap=\"round\" stroke-linejoin=\"round\"> <path d=\"m198.78,196.89l56,-0.45\" id=\"svg_24\"><path> <title><title> <desc>Đoạn thẳng f: Đoạn thẳng [C, A] của Hình đa giác TenDaGiac1<desc> <g> <!-- drawing style --> <g> <!-- clip6 --> <clippath id=\"clip7\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_25\"><path> <clippath> <g clip-path=\"url(#clip7)\" id=\"svg_26\"> <g fill=\"none\" id=\"svg_27\" stroke=\"#993300\" stroke-linecap=\"round\" stroke-linejoin=\"round\"> <path d=\"m254.78,196.44l-28.39,-48.27\" id=\"svg_28\"><path> <title><title> <desc>Đoạn thẳng g: Đoạn thẳng [A, B] của Hình đa giác TenDaGiac1<desc> <g> <!-- drawing style --> <g> <!-- clip7 --> <clippath id=\"clip8\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_29\"><path> <clippath> <g clip-path=\"url(#clip8)\" id=\"svg_30\"> <g fill=\"none\" id=\"svg_31\" stroke=\"#993300\" stroke-linecap=\"round\" stroke-linejoin=\"round\"> <path d=\"m226.39,148.17l-27.61,48.72\" id=\"svg_32\"><path> <title><title> <desc>Đoạn thẳng h: Đoạn thẳng [B, C] của Hình đa giác TenDaGiac1<desc> <g> <!-- drawing style --> <g> <!-- clip8 --> <clippath id=\"clip9\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_33\"><path> <clippath> <g clip-path=\"url(#clip9)\" id=\"svg_34\"> <g fill=\"none\" id=\"svg_35\" stroke=\"#000000\" stroke-linecap=\"round\" stroke-linejoin=\"round\"> <path d=\"m254.78,196.44l28.38,48.28\" id=\"svg_36\"><path> <title><title> <desc>Đoạn thẳng i: Đoạn thẳng [A, D]<desc> <g> <!-- drawing style --> <g> <!-- clip9 --> <clippath id=\"clip10\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_37\"><path> <clippath> <g clip-path=\"url(#clip10)\" id=\"svg_38\"> <g fill=\"none\" id=\"svg_39\" stroke=\"#000000\" stroke-linecap=\"round\" stroke-linejoin=\"round\"> <path d=\"m226.39,148.17l55.23,-97.44\" id=\"svg_40\"><path> <title><title> <desc>Đoạn thẳng j: Đoạn thẳng [B, E]<desc> <g> <!-- drawing style --> <g> <!-- clip10 --> <clippath id=\"clip11\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_41\"><path> <clippath> <g clip-path=\"url(#clip11)\" id=\"svg_42\"> <g fill=\"none\" id=\"svg_43\" stroke=\"#000000\" stroke-linecap=\"round\" stroke-linejoin=\"round\"> <path d=\"m30.778,198.22l168.002,-1.33\" id=\"svg_44\"><path> <title><title> <desc>Đoạn thẳng k: Đoạn thẳng [F, C]<desc> <g> <!-- drawing style --> <g> <!-- clip11 --> <clippath id=\"clip12\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_45\"><path> <clippath> <g clip-path=\"url(#clip12)\" id=\"svg_46\"> <g fill=\"#0000ff\" fill-rule=\"nonzero\" id=\"svg_47\"> <path d=\"m203.78,196.89c0,2.76 -2.24,5 -5,5c-2.76,0 -5,-2.24 -5,-5c0,-2.76 2.24,-5 5,-5c2.76,0 5,2.24 5,5z\" id=\"svg_48\"><path> <title><title> <desc>C = (30.6, -24.92)<desc> <g> <!-- drawing style --> <g> <!-- clip12 --> <clippath id=\"clip13\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_49\"><path> <clippath> <g clip-path=\"url(#clip13)\" id=\"svg_50\"> <g fill=\"none\" id=\"svg_51\" stroke=\"#000000\" stroke-linecap=\"round\" stroke-linejoin=\"round\"> <path d=\"m203.78,196.89c0,2.76 -2.24,5 -5,5c-2.76,0 -5,-2.24 -5,-5c0,-2.76 2.24,-5 5,-5c2.76,0 5,2.24 5,5z\" id=\"svg_52\"><path> <title><title> <desc>C = (30.6, -24.92)<desc> <g> <!-- drawing style --> <g> <!-- clip13 --> <clippath id=\"clip14\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_53\"><path> <clippath> <g clip-path=\"url(#clip14)\" id=\"svg_54\"> <g fill=\"#0000ff\" fill-rule=\"nonzero\" id=\"svg_55\"> <path d=\"m183.11,216.97l2.28,0.58q-0.72,2.79 -2.58,4.27q-1.86,1.48 -4.54,1.48q-2.77,0 -4.51,-1.14q-1.74,-1.13 -2.65,-3.28q-0.91,-2.15 -0.91,-4.6q0,-2.69 1.03,-4.69q1.02,-2 2.91,-3.03q1.89,-1.03 4.17,-1.03q2.58,0 4.34,1.31q1.76,1.32 2.44,3.69l-2.23,0.53q-0.61,-1.87 -1.74,-2.73q-1.14,-0.86 -2.85,-0.86q-1.99,0 -3.32,0.95q-1.33,0.96 -1.86,2.55q-0.54,1.59 -0.54,3.3q0,2.18 0.63,3.82q0.63,1.64 1.98,2.45q1.36,0.8 2.92,0.8q1.92,0 3.24,-1.1q1.32,-1.1 1.79,-3.27z\" id=\"svg_56\"><path> <title><title> <desc>C = (30.6, -24.92)<desc> <g> <!-- drawing style --> <g> <!-- clip14 --> <clippath id=\"clip15\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_57\"><path> <clippath> <g clip-path=\"url(#clip15)\" id=\"svg_58\"> <g fill=\"#0000ff\" fill-rule=\"nonzero\" id=\"svg_59\"> <path d=\"m259.78,196.44c0,2.77 -2.24,5 -5,5c-2.76,0 -5,-2.23 -5,-5c0,-2.76 2.24,-5 5,-5c2.76,0 5,2.24 5,5z\" id=\"svg_60\"><path> <title><title> <desc>A = (49.73, -24.77)<desc> <g> <!-- drawing style --> <g> <!-- clip15 --> <clippath id=\"clip16\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_61\"><path> <clippath> <g clip-path=\"url(#clip16)\" id=\"svg_62\"> <g fill=\"none\" id=\"svg_63\" stroke=\"#000000\" stroke-linecap=\"round\" stroke-linejoin=\"round\"> <path d=\"m259.78,196.44c0,2.77 -2.24,5 -5,5c-2.76,0 -5,-2.23 -5,-5c0,-2.76 2.24,-5 5,-5c2.76,0 5,2.24 5,5z\" id=\"svg_64\"><path> <title><title> <desc>A = (49.73, -24.77)<desc> <g> <!-- drawing style --> <g> <!-- clip16 --> <clippath id=\"clip17\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_65\"><path> <clippath> <g clip-path=\"url(#clip17)\" id=\"svg_66\"> <g fill=\"#0000ff\" fill-rule=\"nonzero\" id=\"svg_67\"> <path d=\"m258.97,186l6.59,-17.19l2.46,0l7.03,17.19l-2.6,0l-2,-5.2l-7.18,0l-1.89,5.2l-2.41,0zm4.95,-7.06l5.83,0l-1.8,-4.75q-0.81,-2.17 -1.22,-3.57q-0.32,1.66 -0.92,3.29l-1.89,5.03z\" id=\"svg_68\"><path> <title><title> <desc>A = (49.73, -24.77)<desc> <g> <!-- drawing style --> <g> <!-- clip17 --> <clippath id=\"clip18\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_69\"><path> <clippath> <g clip-path=\"url(#clip18)\" id=\"svg_70\"> <g fill=\"#444444\" fill-rule=\"nonzero\" id=\"svg_71\"> <path d=\"m231.39,148.17c0,2.76 -2.24,5 -5,5c-2.76,0 -5,-2.24 -5,-5c0,-2.76 2.24,-5 5,-5c2.76,0 5,2.24 5,5z\" id=\"svg_72\"><path> <title><title> <desc>Điểm B: DaGiac[C, A, 3]<desc> <g> <!-- drawing style --> <g> <!-- clip18 --> <clippath id=\"clip19\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_73\"><path> <clippath> <g clip-path=\"url(#clip19)\" id=\"svg_74\"> <g fill=\"none\" id=\"svg_75\" stroke=\"#000000\" stroke-linecap=\"round\" stroke-linejoin=\"round\"> <path d=\"m231.39,148.17c0,2.76 -2.24,5 -5,5c-2.76,0 -5,-2.24 -5,-5c0,-2.76 2.24,-5 5,-5c2.76,0 5,2.24 5,5z\" id=\"svg_76\"><path> <title><title> <desc>Điểm B: DaGiac[C, A, 3]<desc> <g> <!-- drawing style --> <g> <!-- clip19 --> <clippath id=\"clip20\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_77\"><path> <clippath> <g clip-path=\"url(#clip20)\" id=\"svg_78\"> <g fill=\"#444444\" fill-rule=\"nonzero\" id=\"svg_79\"> <path d=\"m213.77,137l0,-17.19l6.43,0q1.97,0 3.16,0.53q1.19,0.52 1.87,1.61q0.68,1.08 0.68,2.27q0,1.09 -0.61,2.07q-0.6,0.98 -1.8,1.57q1.56,0.45 2.4,1.55q0.83,1.11 0.83,2.61q0,1.2 -0.5,2.24q-0.51,1.04 -1.26,1.6q-0.75,0.56 -1.88,0.85q-1.14,0.29 -2.78,0.29l-6.54,0zm2.26,-9.97l3.72,0q1.52,0 2.17,-0.19q0.86,-0.26 1.3,-0.86q0.44,-0.59 0.44,-1.5q0,-0.86 -0.41,-1.5q-0.41,-0.65 -1.17,-0.89q-0.77,-0.25 -2.61,-0.25l-3.44,0l0,5.19zm0,7.94l4.28,0q1.1,0 1.55,-0.08q0.78,-0.14 1.31,-0.47q0.53,-0.33 0.87,-0.95q0.34,-0.63 0.34,-1.45q0,-0.96 -0.5,-1.67q-0.49,-0.71 -1.36,-1q-0.88,-0.29 -2.52,-0.29l-3.97,0l0,5.91z\" id=\"svg_80\"><path> <title><title> <desc>Điểm B: DaGiac[C, A, 3]<desc> <g> <!-- drawing style --> <g> <!-- clip20 --> <clippath id=\"clip21\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_81\"><path> <clippath> <g clip-path=\"url(#clip21)\" id=\"svg_82\"> <g fill=\"#0000ff\" fill-rule=\"nonzero\" id=\"svg_83\"> <path d=\"m288.16,244.72c0,2.76 -2.24,5 -5,5c-2.76,0 -5,-2.24 -5,-5c0,-2.76 2.24,-5 5,-5c2.76,0 5,2.24 5,5z\" id=\"svg_84\"><path> <title><title> <desc>Điểm D: C xoay bởi góc 120°<desc> <g> <!-- drawing style --> <g> <!-- clip21 --> <clippath id=\"clip22\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_85\"><path> <clippath> <g clip-path=\"url(#clip22)\" id=\"svg_86\"> <g fill=\"none\" id=\"svg_87\" stroke=\"#000000\" stroke-linecap=\"round\" stroke-linejoin=\"round\"> <path d=\"m288.16,244.72c0,2.76 -2.24,5 -5,5c-2.76,0 -5,-2.24 -5,-5c0,-2.76 2.24,-5 5,-5c2.76,0 5,2.24 5,5z\" id=\"svg_88\"><path> <title><title> <desc>Điểm D: C xoay bởi góc 120°<desc> <g> <!-- drawing style --> <g> <!-- clip22 --> <clippath id=\"clip23\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_89\"><path> <clippath> <g clip-path=\"url(#clip23)\" id=\"svg_90\"> <g fill=\"#0000ff\" fill-rule=\"nonzero\" id=\"svg_91\"> <path d=\"m291.86,275l0,-17.19l5.91,0q2.01,0 3.06,0.25q1.48,0.35 2.51,1.24q1.36,1.14 2.04,2.93q0.68,1.79 0.68,4.08q0,1.96 -0.46,3.47q-0.46,1.52 -1.17,2.51q-0.71,0.99 -1.56,1.55q-0.85,0.57 -2.06,0.86q-1.2,0.3 -2.76,0.3l-6.19,0zm2.26,-2.03l3.68,0q1.7,0 2.66,-0.31q0.96,-0.32 1.54,-0.89q0.81,-0.82 1.27,-2.18q0.45,-1.37 0.45,-3.31q0,-2.7 -0.89,-4.15q-0.89,-1.44 -2.16,-1.93q-0.9,-0.36 -2.94,-0.36l-3.61,0l0,13.13z\" id=\"svg_92\"><path> <title><title> <desc>Điểm D: C xoay bởi góc 120°<desc> <g> <!-- drawing style --> <g> <!-- clip23 --> <clippath id=\"clip24\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_93\"><path> <clippath> <g clip-path=\"url(#clip24)\" id=\"svg_94\"> <g fill=\"#0000ff\" fill-rule=\"nonzero\" id=\"svg_95\"> <path d=\"m286.62,50.73c0,2.761 -2.24,5 -5,5c-2.76,0 -5,-2.239 -5,-5c0,-2.761 2.24,-5 5,-5c2.76,0 5,2.239 5,5z\" id=\"svg_96\"><path> <title><title> <desc>Điểm E: D xoay bởi góc 120°<desc> <g> <!-- drawing style --> <g> <!-- clip24 --> <clippath id=\"clip25\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_97\"><path> <clippath> <g clip-path=\"url(#clip25)\" id=\"svg_98\"> <g fill=\"none\" id=\"svg_99\" stroke=\"#000000\" stroke-linecap=\"round\" stroke-linejoin=\"round\"> <path d=\"m286.62,50.73c0,2.761 -2.24,5 -5,5c-2.76,0 -5,-2.239 -5,-5c0,-2.761 2.24,-5 5,-5c2.76,0 5,2.239 5,5z\" id=\"svg_100\"><path> <title><title> <desc>Điểm E: D xoay bởi góc 120°<desc> <g> <!-- drawing style --> <g> <!-- clip25 --> <clippath id=\"clip26\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_101\"><path> <clippath> <g clip-path=\"url(#clip26)\" id=\"svg_102\"> <g fill=\"#0000ff\" fill-rule=\"nonzero\" id=\"svg_103\"> <path d=\"m287.91,41l0,-17.188l12.42,0l0,2.032l-10.16,0l0,5.265l9.5,0l0,2.016l-9.5,0l0,5.844l10.55,0l0,2.031l-12.81,0z\" id=\"svg_104\"><path> <title><title> <desc>Điểm E: D xoay bởi góc 120°<desc> <g> <!-- drawing style --> <g> <!-- clip26 --> <clippath id=\"clip27\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_105\"><path> <clippath> <g clip-path=\"url(#clip27)\" id=\"svg_106\"> <g fill=\"#0000ff\" fill-rule=\"nonzero\" id=\"svg_107\"> <path d=\"m35.778,198.22c0,2.76 -2.239,5 -5,5c-2.762,0 -5,-2.24 -5,-5c0,-2.76 2.238,-5 5,-5c2.761,0 5,2.24 5,5z\" id=\"svg_108\"><path> <title><title> <desc>Điểm F: E xoay bởi góc 120°<desc> <g> <!-- drawing style --> <g> <!-- clip27 --> <clippath id=\"clip28\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_109\"><path> <clippath> <g clip-path=\"url(#clip28)\" id=\"svg_110\"> <g fill=\"none\" id=\"svg_111\" stroke=\"#000000\" stroke-linecap=\"round\" stroke-linejoin=\"round\"> <path d=\"m35.778,198.22c0,2.76 -2.239,5 -5,5c-2.762,0 -5,-2.24 -5,-5c0,-2.76 2.238,-5 5,-5c2.761,0 5,2.24 5,5z\" id=\"svg_112\"><path> <title><title> <desc>Điểm F: E xoay bởi góc 120°<desc> <g> <!-- 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