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Omni-MATH / In a triangle ABC, points M and N are on sides AB and AC, respectively, such that MB=BC=CN. Let R and r denote the circumradius and the inradius of the triangle ABC, respectively. …

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problem

In a triangle ABCABC, points MM and NN are on sides ABAB and ACAC, respectively, such that MB=BC=CNMB = BC = CN. Let RR and rr denote the circumradius and the inradius of the triangle ABCABC, respectively. Express the ratio MN/BCMN/BC in terms of RR and rr.
Plain-text mathematical notation (without MathML)
In a triangle ABC, points M and N are on sides AB and AC, respectively, such that MB=BC=CN. Let R and r denote the circumradius and the inradius of the triangle ABC, respectively. Express the ratio MN/BC in terms of R and r.
Original LaTeX notation
In a triangle $ABC$, points $M$ and $N$ are on sides $AB$ and $AC$, respectively, such that $MB = BC = CN$. Let $R$ and $r$ denote the circumradius and the inradius of the triangle $ABC$, respectively. Express the ratio $MN/BC$ in terms of $R$ and $r$.

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task_id
e5ae8ba5-fe8a-5aa0-a671-62dccd9b9196
task_key
test--e5ae8ba5-fe8a-5aa0-a671-62dccd9b9196
task_revision_id
1
config / split
/ test

Official source

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