{"status": "success", "data": {"description_md": "Let there be a circle with radius $5$ centered of $O$. Construct two lines that are externally tangent to the circle at $A$ and $B$. The two lines intersect at a point $C$, and the smallest angle that the two lines create is equal to $30^\\circ$. The smallest possible area of quadrilateral $AOBC$ can be expressed as $a-b\\sqrt{c}$, where $a,b$ and $c$ are positive integers and $c$ is not divisible by the square of any prime. Compute $a+b+c$.", "description_html": "<p>Let there be a circle with radius <span class=\"katex--inline\">5</span> centered of <span class=\"katex--inline\">O</span>. Construct two lines that are externally tangent to the circle at <span class=\"katex--inline\">A</span> and <span class=\"katex--inline\">B</span>. The two lines intersect at a point <span class=\"katex--inline\">C</span>, and the smallest angle that the two lines create is equal to <span class=\"katex--inline\">30^\\circ</span>. The smallest possible area of quadrilateral <span class=\"katex--inline\">AOBC</span> can be expressed as <span class=\"katex--inline\">a-b\\sqrt{c}</span>, where <span class=\"katex--inline\">a,b</span> and <span class=\"katex--inline\">c</span> are positive integers and <span class=\"katex--inline\">c</span> is not divisible by the square of any prime. Compute <span class=\"katex--inline\">a+b+c</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "March Break 2024 - Problem 2", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}