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1975 USAMO Problems/Problem 4

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Problem

Two given circles intersect in two points P and Q. Show how to construct a segment AB passing through P and terminating on the two circles such that AP\cdot PB is a maximum.

size(150);defaultpen(fontsize(7));pair A=(0,0), B=(10,0), P=(4,0), Q=(3.7,-2.5);draw(A--B);draw(circumcircle(A,P,Q));draw(cir...

Solution

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See also

1975 USAMO (Problems)
Preceded by
Problem 3 		1 • 2 • 3 • 4 • 5 Followed by
Problem 5
All USAMO Problems and Solutions
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