Problem

TxO Math Bowl 2024 - Individuals A - Problem 11

$\triangle ABC$ satisfies $AB = AC$ , and has circumcircle $\omega$ . A point $P$ lies on the arc $BC$ not containing $A$ such that $PB < PC$ . Let $Q$ be the reflection of $P$ over point $B$ , and suppose that $\overline{AQ} \perp \overline{BQ}$ . Given that $AB = 7$ and $AQ = 5$ , the area of $\triangle ABC$ can be expressed as $\frac{a\sqrt{b}}{c}$ , where $a$ , $b$ , and $c$ are positive integers such that $a$ and $c$ are relatively prime, and $b$ is not divisible by the square of any prime, find $a + b + c$ .

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Problem Tags: 2-d Geometry Number theory

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Category: TxO Math Bowl Individual Round
Points: 5
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