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Vietnam TST 2017 problem 4

Source: Vietnam TST 2017

March 26, 2017
geometryVietnamTST

Problem Statement

Triangle ABCABC is inscribed in circle (O)(O). AA varies on (O)(O) such that AB>BCAB>BC. MM is the midpoint of ACAC. The circle with diameter BMBM intersects (O)(O) at RR. RMRM intersects (O)(O) at QQ and intersects BCBC at PP. The circle with diameter BPBP intersects AB,BOAB, BO at K,SK,S in this order. a. Prove that SRSR passes through the midpoint of KPKP. b. Let NN be the midpoint of BCBC. The radical axis of circles with diameters AN,BMAN, BM intersects SRSR at EE. Prove that MEME always passes through a fixed point.
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