2007 iTest Problems/Problem 60

Problem

Let $T=\text{TNFTPP}$ . Triangle $ABC$ has $AB=6T-3$ and $AC=7T+1$ . 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

2007 iTest (Problems, Answer Key)
Preceded by: Problem 59	Followed by: Problem TB1
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2007 iTest Problems/Problem 60

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Solution

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