1986 USAMO Problems/Problem 4

Problem

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

Solution

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1986 USAMO (Problems • Resources)
Preceded by Problem 3	Followed by Problem 5
1 • 2 • 3 • 4 • 5
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1986 USAMO Problems/Problem 4

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