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segment tangent to incircle of 5-12-13 triangl 2020 BMT Individual Tiebreakers 3

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January 6, 2022
geometryincircleright triangle

Problem Statement

△ABC\vartriangle ABC has AB=5AB = 5, BC=12BC = 12, and AC=13AC = 13. A circle is inscribed in △ABC\vartriangle ABC, and MNMN tangent to the circle is drawn such that MM is on AC‾\overline{AC}, NN is on BC‾\overline{BC}, and MN‾∥AB‾\overline{MN} \parallel \overline{AB}. The area of △MNC\vartriangle MNC is m/nm/n , where mm and nn are relatively prime positive integers. Find m+nm + n.
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