Difference between revisions of "Mock AIME 1 Pre 2005 Problems/Problem 10"
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== Problem == | == Problem == | ||
<math>ABCDEFG</math> is a regular heptagon inscribed in a unit circle centered at <math>O</math>. <math>l</math> is the line tangent to the circumcircle of <math>ABCDEFG</math> at <math>A</math>, and <math>P</math> is a point on <math>l</math> such that triangle <math>AOP</math> is isosceles. Let <math>p</math> denote the value of <math>AP \cdot BP \cdot CP \cdot DP \cdot EP \cdot FP \cdot GP</math>. Determine the value of <math>p^2</math>. | <math>ABCDEFG</math> is a regular heptagon inscribed in a unit circle centered at <math>O</math>. <math>l</math> is the line tangent to the circumcircle of <math>ABCDEFG</math> at <math>A</math>, and <math>P</math> is a point on <math>l</math> such that triangle <math>AOP</math> is isosceles. Let <math>p</math> denote the value of <math>AP \cdot BP \cdot CP \cdot DP \cdot EP \cdot FP \cdot GP</math>. Determine the value of <math>p^2</math>. | ||
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== See also == | == See also == | ||
{{Mock AIME box|year=Pre 2005|n=1|num-b=9|num-a=11|source=14769}} | {{Mock AIME box|year=Pre 2005|n=1|num-b=9|num-a=11|source=14769}} | ||
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Latest revision as of 00:28, 23 December 2023
Problem
is a regular heptagon inscribed in a unit circle centered at
.
is the line tangent to the circumcircle of
at
, and
is a point on
such that triangle
is isosceles. Let
denote the value of
. Determine the value of
.
See also
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 |