Difference between revisions of "2010-2011 Mock USAJMO Problems/Solutions/Problem 1"
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| + | == 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. | coordinate bash with the origin as the midpoint of BC using Power of a Point. | ||
Revision as of 18:48, 28 June 2015
Problem
Given two fixed, distinct points 
and 
on plane 
, find the locus of all points 
belonging to such that the quadrilateral formed by point , the midpoint of 
, the centroid of 
, and the midpoint of 
(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.
