{"status": "success", "data": {"description_md": "**POTD April 6, 2024**\n\nLet $ABCD$ be an isosceles trapezoid such that $AB = 10, BC = 15,CD = 28,$ and $DA = 15.$ There is a point $E$ such that $\\triangle AED$ and $\\triangle AEB$ have the same area and such that $EC$ is minimal. If $EC$ can be expressed as $\\frac{a}{\\sqrt b},$ with $a,b$ positive integers and $b$ not divisible by the square of any prime, find $a+b$.", "description_html": "<p><strong>POTD April 6, 2024</strong></p>&#10;<p>Let <span class=\"katex--inline\">ABCD</span> be an isosceles trapezoid such that <span class=\"katex--inline\">AB = 10, BC = 15,CD = 28,</span> and <span class=\"katex--inline\">DA = 15.</span> There is a point <span class=\"katex--inline\">E</span> such that <span class=\"katex--inline\">\\triangle AED</span> and <span class=\"katex--inline\">\\triangle AEB</span> have the same area and such that <span class=\"katex--inline\">EC</span> is minimal. If <span class=\"katex--inline\">EC</span> can be expressed as <span class=\"katex--inline\">\\frac{a}{\\sqrt b},</span> with <span class=\"katex--inline\">a,b</span> positive integers and <span class=\"katex--inline\">b</span> not divisible by the square of any prime, find <span class=\"katex--inline\">a+b</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Problem of the Day #119", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}