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Omni-MATH / Let ω₁ be a circle of radius 5, and let ω₂ be a circle of radius 2 whose center lies on ω₁. Let the two circles intersect at A and B, and let the tangents to ω₂ at A and B intersec…

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problem

Let ω1\omega_{1} be a circle of radius 5, and let ω2\omega_{2} be a circle of radius 2 whose center lies on ω1\omega_{1}. Let the two circles intersect at AA and BB, and let the tangents to ω2\omega_{2} at AA and BB intersect at PP. If the area of △ABP\triangle ABP can be expressed as abc\frac{a \sqrt{b}}{c}, where bb is square-free and a,ca, c are relatively prime positive integers, compute 100a+10b+c100a+10b+c.
Plain-text mathematical notation (without MathML)
Let ω₁ be a circle of radius 5, and let ω₂ be a circle of radius 2 whose center lies on ω₁. Let the two circles intersect at A and B, and let the tangents to ω₂ at A and B intersect at P. If the area of △ABP can be expressed as (a√(b))/(c), where b is square-free and a,c are relatively prime positive integers, compute 100a+10b+c.
Original LaTeX notation
Let $\omega_{1}$ be a circle of radius 5, and let $\omega_{2}$ be a circle of radius 2 whose center lies on $\omega_{1}$. Let the two circles intersect at $A$ and $B$, and let the tangents to $\omega_{2}$ at $A$ and $B$ intersect at $P$. If the area of $\triangle ABP$ can be expressed as $\frac{a \sqrt{b}}{c}$, where $b$ is square-free and $a, c$ are relatively prime positive integers, compute $100a+10b+c$.

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Source and history

task_id
11a6c8d2-28cd-510a-9c57-2c01e6e220d6
task_key
test--11a6c8d2-28cd-510a-9c57-2c01e6e220d6
task_revision_id
1
config / split
/ test

Official source

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