Maths tangent properties MC－香港特色

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Maths tangent properties MC

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1. figure: http://img689.imageshack.us/img689/5176/86139305.jpgIn the figure, the circle PQR is inscribed in trainagle ABC. If BR = 3 cm, AP = 4 cm and CQ = 5 cm, find the perimeter of triangle ABC.A 20 cmB 24 cmC 28 cmD 32 cmE 36 cm2. figure: ... 顯示更多 1. figure: http://img689.imageshack.us/img689/5176/86139305.jpg In the figure, the circle PQR is inscribed in trainagle ABC. If BR = 3 cm, AP = 4 cm and CQ = 5 cm, find the perimeter of triangle ABC. A 20 cm B 24 cm C 28 cm D 32 cm E 36 cm 2. figure: http://img163.imageshack.us/img163/7886/16731300.jpg In the figure, TA, TB and PQR are tangents to the circle. If TR = 9 cm, QR = 5 cm and QP = 3 cm, find the length of TP. A 11 cm B 12 cm C 13 cm D 14 cm E 15 cm 3. figure: http://img691.imageshack.us/img691/5985/78931919.jpg In the figure, TA and TC are tangents to the semi-circle. If angle ATC = 56, find the value of x. A. 22 B 24 C 26 D 28 E 30 4. figure: http://img576.imageshack.us/img576/7185/97550402.jpg In the figure, AT is a tangent to the circle. If AT = 8 cm and AB = 2 cm, find the radius of the circle. A 11 cm B 12 cm C 13 cm D 14 cm E 15 cm

最佳解答:

1B 2A 3D 4E STEPS 後補 2010-08-25 22:02:05 補充： Q1) CP=QC=5(tangent prop.) AP=AR=4(tangent prop.) BQ=BR=3(tangent prop.) perimeter = 2*(3+4+5) = 24 cm Q2) QR=AR=5(tangent prop.) BP=PQ=3(tangent prop.) BT=AT(tangent prop.) BP+PT=AR+RT 3+PT=5+9 PT = 11 cm 2010-08-25 22:04:13 補充： Q3) AT=CT(tangent prop.) 角TCA=角TAC(base angle of isos. triangle) 角TAC+角TCA+56度=180度(angle sum of triangle) 角TCA=62度角ACB=90度(angle in semi-circle) x+90度+62度=180度(angle at st. line) x = 28度 Q4) let radius be x, ATO=90度(tangent. prop) AT^2+OT^2=AO^2 64+x^2=(x+2)^2 x^2+64=x^2+4x+4 4x=60 x=15

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