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Omni-MATH / Triangle ABC has side lengths AB=19,BC=20, and CA=21. Points X and Y are selected on sides AB and AC, respectively, such that AY=XY and XY is tangent to the incircle of △ABC. If th…

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problem

Triangle ABCABC has side lengths AB=19,BC=20AB=19, BC=20, and CA=21CA=21. Points XX and YY are selected on sides ABAB and ACAC, respectively, such that AY=XYAY=XY and XYXY is tangent to the incircle of △ABC\triangle ABC. If the length of segment AXAX can be written as ab\frac{a}{b}, where aa and bb are relatively prime positive integers, compute 100a+b100 a+b.
Plain-text mathematical notation (without MathML)
Triangle ABC has side lengths AB=19,BC=20, and CA=21. Points X and Y are selected on sides AB and AC, respectively, such that AY=XY and XY is tangent to the incircle of △ABC. If the length of segment AX can be written as (a)/(b), where a and b are relatively prime positive integers, compute 100a+b.
Original LaTeX notation
Triangle $ABC$ has side lengths $AB=19, BC=20$, and $CA=21$. Points $X$ and $Y$ are selected on sides $AB$ and $AC$, respectively, such that $AY=XY$ and $XY$ is tangent to the incircle of $\triangle ABC$. If the length of segment $AX$ can be written as $\frac{a}{b}$, where $a$ and $b$ are relatively prime positive integers, compute $100 a+b$.

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Source and history

task_id
18772973-b19f-580c-b5d6-8ebf3d251d42
task_key
test--18772973-b19f-580c-b5d6-8ebf3d251d42
task_revision_id
1
config / split
/ test

Official source

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