{"status": "success", "data": {"description_md": "Points $A$ and $B$ are on a circle with center $O$ such that $AB=20$. Point $M$ is the midpoint of the chord $AB$. The perpendicular bisector of $AB$ intersects the circle at $C$ and $D$. If $CM=10$, find $MD$.  \n  \n$\\textbf{(A)}~8 \\qquad \\textbf{(B)}~10 \\qquad \\textbf{(C)}~12 \\qquad \\textbf{(D)}~14 \\qquad \\textbf{(E)}~16$", "description_html": "<p>Points <span class=\"katex--inline\">A</span> and <span class=\"katex--inline\">B</span> are on a circle with center <span class=\"katex--inline\">O</span> such that <span class=\"katex--inline\">AB=20</span>. Point <span class=\"katex--inline\">M</span> is the midpoint of the chord <span class=\"katex--inline\">AB</span>. The perpendicular bisector of <span class=\"katex--inline\">AB</span> intersects the circle at <span class=\"katex--inline\">C</span> and <span class=\"katex--inline\">D</span>. If <span class=\"katex--inline\">CM=10</span>, find <span class=\"katex--inline\">MD</span>.</p>&#10;<p><span class=\"katex--inline\">\\textbf{(A)}~8 \\qquad \\textbf{(B)}~10 \\qquad \\textbf{(C)}~12 \\qquad \\textbf{(D)}~14 \\qquad \\textbf{(E)}~16</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 2, "problem_name": "2024 Mock AMC 10 - Problem 3", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}