View source for 2010-2011 Mock USAJMO Problems/Solutions/Problem 1

== Problem ==

Given two fixed, distinct points <math>B</math> and <math>C</math> on plane <math>\mathcal{P}</math>, find the locus of all points <math>A</math> belonging to <math>\mathcal{P}</math> such that the quadrilateral formed by point <math>A</math>, the midpoint of <math>AB</math>, the centroid of <math>\triangle ABC</math>, and the midpoint of <math>AC</math> (in that order) can be inscribed in a circle.

== Solution ==

Coordinate bash with the origin as the midpoint of BC using Power of a Point.

[[2010-2011 Mock USAJMO Problems/Solutions]]