MathDB
With Geogebra, geometry is easy

Source: Southern Summer School, gr. 11

July 9, 2017
geometryLocusLocus problems

Problem Statement

Let ABCABC be a triangle. A point PP varies inside BCBC. Let Q,RQ, R be the points on AC,ABAC, AB in that order, such that PQ∥AB,PR∥ACPQ\parallel AB, PR\parallel AC. 1. Prove that, when PP varies, the circumcircle of triangle AQRAQR always passes through a fixed point XX other than AA. 2. Extend AXAX so that it cuts the circumcircle of ABCABC a second time at point KK. Prove that AX=XKAX=XK.
Back to ProblemsView on AoPS