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Omni-MATH / In triangle ABC with AB=8 and AC=10, the incenter I is reflected across side AB to point X and across side AC to point Y. Given that segment XY bisects AI, compute BC².

Problem

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problem

In triangle ABCA B C with AB=8A B=8 and AC=10A C=10, the incenter II is reflected across side ABA B to point XX and across side ACA C to point YY. Given that segment XYX Y bisects AIA I, compute BC2B C^{2}.
Plain-text mathematical notation (without MathML)
In triangle ABC with AB=8 and AC=10, the incenter I is reflected across side AB to point X and across side AC to point Y. Given that segment XY bisects AI, compute BC².
Original LaTeX notation
In triangle $A B C$ with $A B=8$ and $A C=10$, the incenter $I$ is reflected across side $A B$ to point $X$ and across side $A C$ to point $Y$. Given that segment $X Y$ bisects $A I$, compute $B C^{2}$.

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Source and history

task_id
63496f5f-6b08-5951-943c-424d6eb5ea08
task_key
test--63496f5f-6b08-5951-943c-424d6eb5ea08
task_revision_id
1
config / split
/ test

Official source

initial import