MathDB
Prove equal fractions

Source: CGMO 2016 Q7

August 14, 2016
geometryincentercircumcircle

Problem Statement

In acute triangle ABC,AB<ACABC, AB<AC, II is its incenter, DD is the foot of perpendicular from II to BCBC, altitude AHAH meets BI,CIBI,CI at P,QP,Q respectively. Let OO be the circumcenter of △IPQ\triangle IPQ, extend AOAO to meet BCBC at LL. Circumcircle of △AIL\triangle AIL meets BCBC again at NN. Prove that BDCD=BNCN\frac{BD}{CD}=\frac{BN}{CN}.
Back to ProblemsView on AoPS