{"status": "success", "data": {"description_md": "Let $\\triangle ABC$ be a scalene triangle. Point $P$ lies on $\\overline{BC}$ so that $\\overline{AP}$ bisects $\\angle BAC.$ The line through $B$ perpendicular to $\\overline{AP}$ intersects the line through $A$ parallel to $\\overline{BC}$ at point $D.$ Suppose $BP=2$ and $PC=3.$ What is $AD?$\n\n$\\textbf{(A) } 8 \\qquad \\textbf{(B) } 9 \\qquad \\textbf{(C) } 10 \\qquad \\textbf{(D) } 11 \\qquad \\textbf{(E) } 12$", "description_html": "<p>Let  <span class=\"katex--inline\">\\triangle ABC</span>  be a scalene triangle. Point  <span class=\"katex--inline\">P</span>  lies on  <span class=\"katex--inline\">\\overline{BC}</span>  so that  <span class=\"katex--inline\">\\overline{AP}</span>  bisects  <span class=\"katex--inline\">\\angle BAC.</span>  The line through  <span class=\"katex--inline\">B</span>  perpendicular to  <span class=\"katex--inline\">\\overline{AP}</span>  intersects the line through  <span class=\"katex--inline\">A</span>  parallel to  <span class=\"katex--inline\">\\overline{BC}</span>  at point  <span class=\"katex--inline\">D.</span>  Suppose  <span class=\"katex--inline\">BP=2</span>  and  <span class=\"katex--inline\">PC=3.</span>  What is  <span class=\"katex--inline\">AD?</span> </p>\n<p> <span class=\"katex--inline\">\\textbf{(A) } 8 \\qquad \\textbf{(B) } 9 \\qquad \\textbf{(C) } 10 \\qquad \\textbf{(D) } 11 \\qquad \\textbf{(E) } 12</span> </p>\n<hr><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>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2022 AMC 10A Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/22_amc10A_p14", "prev": "/problem/22_amc10A_p12"}}