MathDB
equal segments iff 3 points are collinear, 3 circles related

Source: KJMO 2011 p2

May 3, 2019
geometryequal segmentscollinearcollinearitycirclescyclic quadrilateral

Problem Statement

Let ABCDABCD be a cyclic quadrilateral inscirbed in circle OO. Let the tangent to OO at AA meet BCBC at SS, and the tangent to OO at BB meet CDCD at TT. Circle with SS as its center and passing AA meets BCBC at EE, and AEAE meets OO again at F(≠A)F(\ne A). The circle with TT as its center and passing BB meets CDCD at KK. Let P=BK∩ACP = BK \cap AC. Prove that P,F,DP,F,D are collinear if and only if AB=APAB = AP.
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