2007 iTest Problems/Problem 60

The following problem is from the Ultimate Question of the 2007 iTest, where solving this problem required the answer of a previous problem. When the problem is rewritten, the T-value is substituted.

Problem

Triangle $ABC$ has $AB=99$ and $AC=120$. Point $D$ is on $BC$ so that $AD$ bisects angle $BAC$. The circle through $A, B$, and $D$ has center $O_1$ and intersects line $AC$ again at $B'$, and likewise the circle through $A, C$, and $D$ has center $O_2$ and intersects line $AB$ again at $C'$. If the four points $B', C', O_1$, and $O_2$ lie on a circle, find the length of $BC$.

Solution

111

See Also

2007 iTest (Problems, Answer Key)
Preceded by:
Problem 59
Followed by:
Problem TB1
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