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PT is perpendicular to XY

Source: Iran TST 2005

April 20, 2005
geometrycircumcircleratioparallelogramsymmetrygeometric transformationreflection

Problem Statement

Assume ABCABC is an isosceles triangle that AB=ACAB=AC Suppose PP is a point on extension of side BCBC. XX and YY are points on ABAB and ACAC that: PX∣∣AC , PY∣∣ABPX || AC \ , \ PY ||AB Also TT is midpoint of arc BCBC. Prove that PT⊥XYPT \perp XY
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