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Double parallel lines

Source: BdMO 2023 Secondary National P6

February 12, 2023
geometrycyclic quadrilateralAngle Chasing

Problem Statement

Let △ABC\triangle ABC be an acute angle triangle and ω\omega be its circumcircle. Let NN be a point on arc ACAC not containing BB and SS be a point on line ABAB. The line tangent to ω\omega at NN intersects BCBC at TT, NSNS intersects ω\omega at KK. Assume that ∠NTC=∠KSB\angle NTC = \angle KSB. Prove that CK∥AN∥TSCK\parallel AN \parallel TS.
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