{"status": "success", "data": {"description_md": "**POTD July 14, 2024**\n\nTriangle $ABC$ has altitudes $AD$, $BE$, and $CF$. The distances from $A$ to $EF$, $B$ to $DF$, and $C$ to $DE$ are $2$, $3$, and $6$, respectively. Find the area of $DEF$.", "description_html": "<p><strong>POTD July 14, 2024</strong></p>&#10;<p>Triangle <span class=\"katex--inline\">ABC</span> has altitudes <span class=\"katex--inline\">AD</span>, <span class=\"katex--inline\">BE</span>, and <span class=\"katex--inline\">CF</span>. The distances from <span class=\"katex--inline\">A</span> to <span class=\"katex--inline\">EF</span>, <span class=\"katex--inline\">B</span> to <span class=\"katex--inline\">DF</span>, and <span class=\"katex--inline\">C</span> to <span class=\"katex--inline\">DE</span> are <span class=\"katex--inline\">2</span>, <span class=\"katex--inline\">3</span>, and <span class=\"katex--inline\">6</span>, respectively. Find the area of <span class=\"katex--inline\">DEF</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "Problem of the Day #217", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}