MathDB

1

Part of 2017 OMMock - Mexico National Olympiad Mock Exam

Problems(1)

Segment equality with a rhombus

Source: Mexico National Olympiad Mock Exam 2017 P1

11/2/2019
Let ABCABC be a triangle with circumcenter OO. Point D,E,FD, E, F are chosen on sides AB,BCAB, BC and ACAC, respectively, such that ADEFADEF is a rhombus. The circumcircles of BDEBDE and CFECFE intersect AEAE at PP and QQ respectively. Show that OP=OQOP=OQ.
Proposed by Ariel García
geometryCircumcenterrhombuscircumcircle