{"status": "success", "data": {"description_md": "**POTD December 8, 2023**\n**Author:** qgek\n\nIn the unit cube $ABCD- A_1B_1C_1D_1,$ point P is the midpoint of $CC_1$, and point $Q$ is the midpoint of $A_1B_1$. Point $M$ lies on segment $AD$, and $AM : MD = 2 : 1$. The plane $MQP$ intersects $B_1C_1$ at point H. If the area of $\\triangle BHP = \\frac{m}{n}$, where $m$ and $n$ are positive coprime integers, find $m + n$.", "description_html": "<p><strong>POTD December 8, 2023</strong><br/>&#10;<strong>Author:</strong> qgek</p>&#10;<p>In the unit cube <span class=\"katex--inline\">ABCD- A_1B_1C_1D_1,</span> point P is the midpoint of <span class=\"katex--inline\">CC_1</span>, and point <span class=\"katex--inline\">Q</span> is the midpoint of <span class=\"katex--inline\">A_1B_1</span>. Point <span class=\"katex--inline\">M</span> lies on segment <span class=\"katex--inline\">AD</span>, and <span class=\"katex--inline\">AM : MD = 2 : 1</span>. The plane <span class=\"katex--inline\">MQP</span> intersects <span class=\"katex--inline\">B_1C_1</span> at point H. If the area of <span class=\"katex--inline\">\\triangle BHP = \\frac{m}{n}</span>, where <span class=\"katex--inline\">m</span> and <span class=\"katex--inline\">n</span> are positive coprime integers, find <span class=\"katex--inline\">m + n</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Problem of the Day #19", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}