MathDB

4

Part of 1986 USAMO

Problems(1)

1986 USAMO Problem #4

Source:

8/16/2011
Two distinct circles K1K_1 and K2K_2 are drawn in the plane. They intersect at points AA and BB, where ABAB is the diameter of K1K_1. A point PP on K2K_2 and inside K1K_1 is also given.
Using only a "T-square" (i.e. an instrument which can produce a straight line joining two points and the perpendicular to a line through a point on or off the line), find a construction for two points CC and DD on K1K_1 such that CDCD is perpendicular to ABAB and ∠CPD\angle CPD is a right angle.
AMCUSA(J)MOUSAMOgeometry unsolvedgeometry