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2

Part of 1998 Nordic

Problems(1)

rectangle out of 2 circles & perpendiculars

Source: Nordic Mathematical Contest 1998 #2

10/3/2017
Let C1C_1 and C2C_2 be two circles intersecting at AA and BB. Let SS and TT be the centres of C1C_1 and C2C_2, respectively. Let PP be a point on the segment ABAB such that ∣AP∣≠∣BP∣ |AP|\ne |BP| and P≠A,P≠BP\ne A, P \ne B. We draw a line perpendicular to SPSP through PP and denote by CC and DD the points at which this line intersects C1C_1. We likewise draw a line perpendicular to TPTP through PP and denote by EE and F the points at which this line intersects C2C_2. Show that C,D,E,C, D, E, and FF are the vertices of a rectangle.
geometryrectangle