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MATH QUESTION CIRCLES 4

發問:

圖片參考：http://imgcld.yimg.com/8/n/HA00610265/o/701010110125213873376900.jpg IN THE FOLLOWING FIGURE, O is the centre. 16. In the figure, AB is a diameter. PB and PC are the tangents to the circle at B and C respectively. Prove that AC//OP.

最佳解答:

PO = PO (common) OC = OB (radius) ㄥPCO = ㄥPBO = 90° (tangent⊥radius)△POC =~= △POB (R.H.S.)We let ㄥPOC = ㄥPOB = x ,then ㄥCOA = 180° - 2x ,ㄥACO = (180° - ㄥCOA)/2 = (180 - (180° - 2x ))/2 = x= ㄥPOCHence AC//OP (alt.∠s equal)

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