MathDB
Isoceles triangle [Iran TST 2010]

Source:

May 10, 2010
geometrycircumcircletrapezoidgeometry proposed

Problem Statement

Let ABCABC an isosceles triangle and BC>AB=ACBC>AB=AC. D,MD,M are respectively midpoints of BC,ABBC, AB. XX is a point such that BX⊥ACBX\perp AC and XD∣∣ABXD||AB. BXBX and ADAD meet at HH. If PP is intersection point of DXDX and circumcircle of AHXAHX (other than XX), prove that tangent from AA to circumcircle of triangle AMPAMP is parallel to BCBC.
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