MathDB
locus of P as M moves on major arc AB of the larger circle

Source: China TST 1995, problem 2

May 17, 2005
geometrygeometric transformationgeometry unsolvedTangentsLocus problemsChinaTST

Problem Statement

Given a fixed acute angle θ\theta and a pair of internally tangent circles, let the line ll which passes through the point of tangency, AA, cut the larger circle again at BB (ll does not pass through the centers of the circles). Let MM be a point on the major arc ABAB of the larger circle, NN the point where AMAM intersects the smaller circle, and PP the point on ray MBMB such that ∠MPN=θ\angle MPN = \theta. Find the locus of PP as MM moves on major arc ABAB of the larger circle.
Back to ProblemsView on AoPS