{"status": "success", "data": {"description_md": "**POTD April 28, 2024**\n\nIn right triangle $ABC$, we have $\\angle A = 90^\\circ$, $AB=3$, $AC=4$. Points $X_1, X_2, \\ldots, X_k$ split $\\overline{BC}$ into $k+1$ segments of equal length. Find the minimum value of $k$ such that the set of lines $\\overline{AX_i}$ contains the angle bisector of $\\angle A$, the $A$-median, and the altitude from $A$ to $\\overline{BC}$.", "description_html": "<p><strong>POTD April 28, 2024</strong></p>&#10;<p>In right triangle <span class=\"katex--inline\">ABC</span>, we have <span class=\"katex--inline\">\\angle A = 90^\\circ</span>, <span class=\"katex--inline\">AB=3</span>, <span class=\"katex--inline\">AC=4</span>. Points <span class=\"katex--inline\">X_1, X_2, \\ldots, X_k</span> split <span class=\"katex--inline\">\\overline{BC}</span> into <span class=\"katex--inline\">k+1</span> segments of equal length. Find the minimum value of <span class=\"katex--inline\">k</span> such that the set of lines <span class=\"katex--inline\">\\overline{AX_i}</span> contains the angle bisector of <span class=\"katex--inline\">\\angle A</span>, the <span class=\"katex--inline\">A</span>-median, and the altitude from <span class=\"katex--inline\">A</span> to <span class=\"katex--inline\">\\overline{BC}</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "Problem of the Day #140", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}