MathForces: Math Olympiads
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Sharingan

Author: mathforces
Problem has been solved: 10 times

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In the equilateral triangle $ ABC $, the point $ X $ was chosen. $ XN $, $ XM $ and $ XL $ are perpendiculars from point $X$ to the sides $ AB $, $ BC $ and $ CA $, respectively. Denote by $ r_{QWE} $ the radius of the inscribed circle of the triangle $ QWE $. It turned out that $r_{XAN}=144$, $r_{XBM}=169$, $r_{XMC}=196$, $r_{XCL}=400$. Find $ r_{XNB} + r_{XLA} $.





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