{"status": "success", "data": {"description_md": "Let a parabola $y=x^2$ and a circle $\\gamma$ share a common tangent at $(1,1)$. If $\\gamma$ is tangent to the positive x-axis and the radius of the circle can be expressed as $\\frac{a-\\sqrt b}{c}$, where $a,b,c$ are positive integers and $b$ is not divisible by the square of any prime, find $a+b+c$.", "description_html": "<p>Let a parabola <span class=\"katex--inline\">y=x^2</span> and a circle <span class=\"katex--inline\">\\gamma</span> share a common tangent at <span class=\"katex--inline\">(1,1)</span>. If <span class=\"katex--inline\">\\gamma</span> is tangent to the positive x-axis and the radius of the circle can be expressed as <span class=\"katex--inline\">\\frac{a-\\sqrt b}{c}</span>, where <span class=\"katex--inline\">a,b,c</span> are 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": 4, "problem_name": "Christmas Contest - Team Round - Problem 18", "can_next": true, "can_prev": true, "nxt": "/problem/christmas1_team-p19", "prev": "/problem/christmas1_team-p17"}}