MathDB
ADG is isosceles

Source: ItaMO 2003, P3

February 13, 2012
geometrygeometric transformationhomothetycircumcirclereflectiongeometry proposed

Problem Statement

Let a semicircle is given with diameter ABAB and centre OO and let CC be a arbitrary point on the segment OBOB. Point DD on the semicircle is such that CDCD is perpendicular to ABAB. A circle with centre PP is tangent to the arc BDBD at FF and to the segment CDCD and ABAB at EE and GG respectively. Prove that the triangle ADGADG is isosceles.
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