{"status": "success", "data": {"description_md": "**POTD August 19, 2024**\n\nAn equilateral triangle is given. A point lies on the incircle of the triangle. The smallest two distances from the point to the sides of the triangle is $1$ and $4$. The sidelength of this triangle can be expressed as $\\frac{a\\sqrt b}{c}$ where $a$ and $c$ are relatively prime positive integers and $b$ is not divisible by the square of any prime. Find $a + b + c$.", "description_html": "<p><strong>POTD August 19, 2024</strong></p>&#10;<p>An equilateral triangle is given. A point lies on the incircle of the triangle. The smallest two distances from the point to the sides of the triangle is <span class=\"katex--inline\">1</span> and <span class=\"katex--inline\">4</span>. The sidelength of this triangle can be expressed as <span class=\"katex--inline\">\\frac{a\\sqrt b}{c}</span> where <span class=\"katex--inline\">a</span> and <span class=\"katex--inline\">c</span> are relatively prime positive integers and <span class=\"katex--inline\">b</span> is not divisible by the square of any prime. Find <span class=\"katex--inline\">a + b + c</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "Problem of the Day #250", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}