MathDB

Problem 10.2

Part of 2007 Bulgarian Autumn Math Competition

Problems(1)

Classic geo

Source: 2007 Bulgarian Autumn Math Competition, Problem 10.2

3/17/2022
Let AC>BCAC>BC in △ABC\triangle ABC and MM and NN be the midpoints of ACAC and BCBC respectively. The angle bisector of ∠B\angle B intersects MN‾\overline{MN} at PP. The incircle of △ABC\triangle ABC has center II and touches BCBC at QQ. The perpendiculars from PP and QQ to MNMN and BCBC respectively intersect at RR. Let S=AB∩RNS=AB\cap RN. a) Prove that PCQIPCQI is cyclic b) Express the length of the segment BSBS with aa, bb, cc - the side lengths of △ABC\triangle ABC .
geometryCyclicangle bisector