MathDB

15

Part of 2011 Sharygin Geometry Olympiad

Problems(1)

quadrilaterals with equal areas, related to tangents from a point to circle

Source: 2011 Sharygin Geometry Olympiad Correspondence Round P15

4/4/2019
Given a circle with center OO and radius equal to 11. ABAB and ACAC are the tangents to this circle from point AA. Point MM on the circle is such that the areas of quadrilaterals OBMCOBMC and ABMCABMC are equal. Find MAMA.
geometrycircleTangentsequal areaquadrilateralarea