MathDB
Segment has Length Equal to Circumradius

Source: 2014 USAMO Problem 5

April 30, 2014
geometrycircumcirclevectorgeometric transformationparallelogramtrigonometrycomplex bash

Problem Statement

Let ABCABC be a triangle with orthocenter HH and let PP be the second intersection of the circumcircle of triangle AHCAHC with the internal bisector of the angle ∠BAC\angle BAC. Let XX be the circumcenter of triangle APBAPB and YY the orthocenter of triangle APCAPC. Prove that the length of segment XYXY is equal to the circumradius of triangle ABCABC.
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