{"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$\\text{(A)}\\ \\dfrac{15}2 \\qquad \\text{(B)}\\ 8 \\qquad \\text{(C)}\\ \\dfrac{17}2 \\qquad \\text{(D)}\\ 9 \\qquad \\text{(E)}\\ \\dfrac{19}2$", "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>&#10;<p><span class=\"katex--inline\">\\text{(A)}\\ \\dfrac{15}2 \\qquad \\text{(B)}\\ 8 \\qquad \\text{(C)}\\ \\dfrac{17}2 \\qquad \\text{(D)}\\ 9 \\qquad \\text{(E)}\\ \\dfrac{19}2</span></p>&#10;", "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"}}