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F5 Maths

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發問:

Figure: http://img8.imageshack.us/img8/4316/38795130.jpg In the figure, AB, BC, CD and DA are tangents to the circle at P, Q , R and S respectively. AD = 16 cm and BC = 20 cm. FInd the perimeter of ABCD.

最佳解答:

Let AS=a, AP=a(tangent properties) Let SD=b, DR=b(tangent properties) Let BQ=c, PB=c(tangent properties)' Let QC=d, RC=d(tangent properties) AS+SD=16 a+b=16 BQ+QC=20 c+d=20 the perimeter of ABCD =(AS+SD)+(AP+PB)+(DR+RC)+(BQ+QC) =16+(a+c)+(b+d)+20 =16+36+20 =72 cm

其他解答:

Let AS, BQ, QC and DS be a, b, c and d respectively. AS=AP=a (tangent prop.) BQ=PB=b (tangent prop.) QC=CR=c (tangent prop.) DS=DR=d (tangent prop.) AS+SD=16 a+d=16 BQ+QC=20 b+c=20 The perimeter of ABCD =AD+BC+AP+PB+RC+DR =16+20+a+b+c+d =36+(a+d)+(b+c) =36+16+20 =72cm