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2017 Iran TST2 P1

Source: 2017 Iran TST second exam day1 p1

April 23, 2017
geometryIranIranian TSTtrapezoidcircumcircle

Problem Statement

ABCDABCD is a trapezoid with AB∥CDAB \parallel CD. The diagonals intersect at PP. Let ω1\omega _1 be a circle passing through BB and tangent to ACAC at AA. Let ω2\omega _2 be a circle passing through CC and tangent to BDBD at DD. ω3\omega _3 is the circumcircle of triangle BPCBPC. Prove that the common chord of circles ω1,ω3\omega _1,\omega _3 and the common chord of circles ω2,ω3\omega _2, \omega _3 intersect each other on ADAD.
Proposed by Kasra Ahmadi
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