{"status": "success", "data": {"description_md": "Points $A,B,C$ and $D$ lie on a line, in that order, with $AB = CD$ and $BC = 12$. Point $E$ is not on the line, and $BE = CE = 10$. The perimeter of $\\triangle AED$ is twice the perimeter of $\\triangle BEC$. Find $AB$.\n\n$\\text{(A)}\\ 15/2 \\qquad \\text{(B)}\\ 8 \\qquad \\text{(C)}\\ 17/2 \\qquad \\text{(D)}\\ 9 \\qquad \\text{(E)}\\ 19/2$", "description_html": "<p>Points  <span class=\"katex--inline\">A,B,C</span>  and  <span class=\"katex--inline\">D</span>  lie on a line, in that order, with  <span class=\"katex--inline\">AB = CD</span>  and  <span class=\"katex--inline\">BC = 12</span> . Point  <span class=\"katex--inline\">E</span>  is not on the line, and  <span class=\"katex--inline\">BE = CE = 10</span> . The perimeter of  <span class=\"katex--inline\">\\triangle AED</span>  is twice the perimeter of  <span class=\"katex--inline\">\\triangle BEC</span> . Find  <span class=\"katex--inline\">AB</span> .</p>\n<p> <span class=\"katex--inline\">\\text{(A)}\\ 15/2 \\qquad \\text{(B)}\\ 8 \\qquad \\text{(C)}\\ 17/2 \\qquad \\text{(D)}\\ 9 \\qquad \\text{(E)}\\ 19/2</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": 4, "problem_name": "2002 AMC 10A Problem 23", "can_next": true, "can_prev": true, "nxt": "/problem/02_amc10A_p24", "prev": "/problem/02_amc10A_p22"}}