{"status": "success", "data": {"description_md": "Consider all triangles $ABC$ satisfying in the following conditions: $AB = AC$, $D$ is a point on $\\overline{AC}$ for which $\\overline{BD} \\perp \\overline{AC}$, $AC$ and $CD$ are integers, and $BD^2 = 57$. Among all such triangles, the smallest possible value of $AC$ is\n\n<center><img class=\"problem-image\" src=\"/static/AHSME/1999/crops/99_ahsme_p19_fig.png\" alt=\"figure\" width=\"242\"></center>\n\n$\\text{(A)}\\ 9\\qquad\\text{(B)}\\ 10\\qquad\\text{(C)}\\ 11\\qquad\\text{(D)}\\ 12\\qquad\\text{(E)}\\ 13$\n\n___\n\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.\n", "description_html": "<p>Consider all triangles <span class=\"katex--inline\">ABC</span> satisfying in the following conditions: <span class=\"katex--inline\">AB = AC</span>, <span class=\"katex--inline\">D</span> is a point on <span class=\"katex--inline\">\\overline{AC}</span> for which <span class=\"katex--inline\">\\overline{BD} \\perp \\overline{AC}</span>, <span class=\"katex--inline\">AC</span> and <span class=\"katex--inline\">CD</span> are integers, and <span class=\"katex--inline\">BD^2 = 57</span>. Among all such triangles, the smallest possible value of <span class=\"katex--inline\">AC</span> is</p>\n<center><img class=\"problem-image\" src=\"/static/AHSME/1999/crops/99_ahsme_p19_fig.png\" alt=\"figure\" width=\"242\"></center>\n<p><span class=\"katex--inline\">\\text{(A)}\\ 9\\qquad\\text{(B)}\\ 10\\qquad\\text{(C)}\\ 11\\qquad\\text{(D)}\\ 12\\qquad\\text{(E)}\\ 13</span></p>\n<hr>\n<p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>\n", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 2, "problem_name": "1999 AHSME Problem 19", "can_next": true, "can_prev": true, "nxt": "/problem/99_ahsme_p20", "prev": "/problem/99_ahsme_p18"}}