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ICSE Class 10 Answered

Two circles intersect at two points A and B. From a point P on a circle, two line segments PAC and PBD are drawn intersecting the other circle at the points C and D. Prove that CD is parallel to tangent at P.
Asked by Topperlearning User | 06 Oct, 2017, 02:35: PM
answered-by-expert Expert Answer

begin mathsize 12px style Mp space is space straight a space tangent space at space straight P Join space AB angle space MPA space equals space angle space PBA space space space space space left parenthesis Angles space in space the space alternate space segment right parenthesis angle space PBA space equals space angle space ACD space space space space space space left parenthesis Exterior space angle space of space straight a space cyclic space quadrilateral space ABCD space is space equal space to space its space interior space opposite space angle right parenthesis angle space MPA space equals angle space ACD rightwards double arrow space angle space MPC space equals space angle space PCD But space these space are space straight a space pair space alternate space interior space angles MP space parallel to space CD. end style

Answered by | 06 Oct, 2017, 04:35: PM
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