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min circumradii wanted, line // BC in triangle ABC

Source: 2005 Oral Moscow Geometry Olympiad grades 10-11 p1

October 21, 2020
geometryradiusparallel

Problem Statement

Given an acute-angled triangle ABCABC. A straight line parallel to BCBC intersects sides ABAB and ACAC at points MM and PP, respectively. At what location of the points MM and PP will the radius of the circle circumscribed about the triangle BMPBMP be the smallest?
(I. Sharygin)
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