View source for 1986 USAMO Problems/Problem 4

==Problem==
Two distinct circles <math>K_1</math> and <math>K_2</math> are drawn in the plane. They intersect at points <math>A</math> and <math>B</math>, where <math>AB</math> is the diameter of <math>K_1</math>. A point <math>P</math> on <math>K_2</math> and inside <math>K_1</math> 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 <math>C</math> and <math>D</math> on <math>K_1</math> such that <math>CD</math> is perpendicular to <math>AB</math> and <math>\angle CPD</math> is a right angle.

==Solution==
{{solution}}

==See Also==

{{USAMO box|year=1986|num-b=3|num-a=5}}
{{MAA Notice}}
[[Category:Olympiad Geometry Problems]]
[[Category:Geometric Construction Problems]]