{"status": "success", "data": {"description_md": "**POTD Normal December 17, 2023**\n**Author:** excelex\n\nA triangle $\\triangle ABC$ is drawn with sides $AB = 13, BC = 14,$ and $AC = 15$. Let $H$ be the orthocentre of $\\triangle ABC$ and $M$ be the midpoint of side $AC$. Point $D$ is drawn on line $HM$ such that $MD = MH$. In other words, $D$ is the reflection of $H$ over $M$. The length of $BD$ can be written as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Compute $m+n$.\n  ", "description_html": "<p><strong>POTD Normal December 17, 2023</strong><br/>&#10;<strong>Author:</strong> excelex</p>&#10;<p>A triangle <span class=\"katex--inline\">\\triangle ABC</span> is drawn with sides <span class=\"katex--inline\">AB = 13, BC = 14,</span> and <span class=\"katex--inline\">AC = 15</span>. Let <span class=\"katex--inline\">H</span> be the orthocentre of <span class=\"katex--inline\">\\triangle ABC</span> and <span class=\"katex--inline\">M</span> be the midpoint of side <span class=\"katex--inline\">AC</span>. Point <span class=\"katex--inline\">D</span> is drawn on line <span class=\"katex--inline\">HM</span> such that <span class=\"katex--inline\">MD = MH</span>. In other words, <span class=\"katex--inline\">D</span> is the reflection of <span class=\"katex--inline\">H</span> over <span class=\"katex--inline\">M</span>. The length of <span class=\"katex--inline\">BD</span> can be written as <span class=\"katex--inline\">\\frac{m}{n}</span>, where <span class=\"katex--inline\">m</span> and <span class=\"katex--inline\">n</span> are relatively prime positive integers. Compute <span class=\"katex--inline\">m+n</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "Problem of the Day #28 (Normal)", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}