{"status": "success", "data": {"description_md": "Point $P$ is on the $y$-axis with $y$-coordinate greater than 0 and less than 100. A circle is drawn through $P$, $Q(4,4)$ and $O(0,0)$. How many possible positions for $P$ are there so that the radius of this circle is an integer?\n\n$\\text{(A)}\\ 2\\qquad\\text{(B)}\\ 68\\qquad\\text{(C)}\\ 66\\qquad\\text{(D)}\\ 65\\qquad\\text{(E)}\\ 67$\n\n___\n\n**[Cayley](https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf), by [CEMC](https://cemc.uwaterloo.ca/), is licensed under the [CC BY-NC 3.0 DEED](https://creativecommons.org/licenses/by-nc/3.0/). They are not affiliated with or endorse TopsOJ in any way.**\n", "description_html": "<p>Point <span class=\"katex--inline\">P</span> is on the <span class=\"katex--inline\">y</span>-axis with <span class=\"katex--inline\">y</span>-coordinate greater than 0 and less than 100. A circle is drawn through <span class=\"katex--inline\">P</span>, <span class=\"katex--inline\">Q(4,4)</span> and <span class=\"katex--inline\">O(0,0)</span>. How many possible positions for <span class=\"katex--inline\">P</span> are there so that the radius of this circle is an integer?</p>\n<p><span class=\"katex--inline\">\\text{(A)}\\ 2\\qquad\\text{(B)}\\ 68\\qquad\\text{(C)}\\ 66\\qquad\\text{(D)}\\ 65\\qquad\\text{(E)}\\ 67</span></p>\n<hr>\n<p><strong><a href=\"https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf\">Cayley</a>, by <a href=\"https://cemc.uwaterloo.ca/\">CEMC</a>, is licensed under the <a href=\"https://creativecommons.org/licenses/by-nc/3.0/\">CC BY-NC 3.0 DEED</a>. They are not affiliated with or endorse TopsOJ in any way.</strong></p>\n", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2014 Cayley Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/14_cayley_p24"}}