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Perpendicular following tangent circles

Source: China Team Selection Test 2016 Test 2 Day 2 Q6

March 21, 2016
geometrycyclic quadrilateralharmonic division

Problem Statement

The diagonals of a cyclic quadrilateral ABCDABCD intersect at PP, and there exist a circle Γ\Gamma tangent to the extensions of AB,BC,AD,DCAB,BC,AD,DC at X,Y,Z,TX,Y,Z,T respectively. Circle Ω\Omega passes through points A,BA,B, and is externally tangent to circle Γ\Gamma at SS. Prove that SP⊥STSP\perp ST.
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