Mock AIME 1 Pre 2005 Problems/Problem 10

Problem

$ABCDEFG$ is a regular heptagon inscribed in a unit circle centered at $O$ . $l$ is the line tangent to the circumcircle of $ABCDEFG$ at $A$ , and $P$ is a point on $l$ such that triangle $AOP$ is isosceles. Let $p$ denote the value of $AP \cdot BP \cdot CP \cdot DP \cdot EP \cdot FP \cdot GP$ . Determine the value of $p^2$ .

Mock AIME 1 Pre 2005 (Problems, Source)
Preceded by Problem 9	Followed by Problem 11
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15

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Mock AIME 1 Pre 2005 Problems/Problem 10

Problem

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