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標題:

F4 math problems ( Circles )

發問:

In Figure, TA,TB and PQ are tangents to the circle. TP = 8cm, TQ = 10cm and BQ = x cm. If Pq = 6cm, find x. Figure http://server5.pictiger.com/img/1090366/picture-hosting/.jpg

最佳解答:

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圖片參考：http://hk.geocities.com/namsm4e/p0121.jpg 計算這題的主要使用的性質是一點至圓的兩條切線距離相等。 所以 TA = TB PA = PR QA = QR 因 BQ = x cm 所以 QR = x cm PR = 6 – x AP = 6 – x TA = 8 + 6 – x TB = 10 + x 因 TA = TB 8 + 6 – x = 10 + x 2x = 4 x = 2cm

其他解答:

AT=BT(tangent properties) BQ=X(Given) AP+8=X+10 AP=X+2 AP=RP(tangent properties) BQ=RQ(tangent properties) RP+RQ=PQ (X+2)+X=6 2X=4 X=2