MathDB
Perpendicular bisector

Source: 2016 Korea Winter Camp 2nd Test #5

January 25, 2016
geometryperpendicular bisector

Problem Statement

Let there be an acute triangle ABCABC with orthocenter HH. Let BH,CHBH, CH hit the circumcircle of △ABC\triangle ABC at D,ED, E. Let PP be a point on ABAB, between BB and the foot of the perpendicular from CC to ABAB. Let PH∩AC=QPH \cap AC = Q. Now △AEP\triangle AEP's circumcircle hits CHCH at SS, △ADQ\triangle ADQ's circumcircle hits BHBH at RR, and △AEP\triangle AEP's circumcircle hits △ADQ\triangle ADQ's circumcircle at J(≠A)J (\not=A). Prove that RSRS is the perpendicular bisector of HJHJ.
Back to ProblemsView on AoPS