1999 AIME Problems/Problem 12
Problem
The inscribed circle of triangle is tangent to at and its radius is 21. Given that and find the perimeter of the triangle.
Solution
Let be the tangency point on , and on . By the Two Tangent Theorem, , , and . Using , where , we get . By Heron's Formula, . Equating and squaring both sides,
$$ (Error compiling LaTeX. Unknown error_msg)\begin{eqnarray*} [21(50+x)]^2 &=& (50+x)(x)(621)\ 441(50+x) &=& 621x\ 180x = 441 \cdot 50 \Longrightarrow x \frac{245}{2} $$ (Error compiling LaTeX. Unknown error_msg)
We want the perimeter, which is .
See also
1999 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 11 |
Followed by Problem 13 | |
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All AIME Problems and Solutions |