{"status": "success", "data": {"description_md": "In $\\triangle ABC$, $AB=6$, $AC=8$, $BC=10$, and $D$ is the midpoint of $\\overline{BC}$. What is the sum of the radii of the circles inscribed in $\\triangle ADB$ and $\\triangle ADC$?\n\n$\\textbf{(A)}\\ \\sqrt{5}\\qquad\\textbf{(B)}\\ \\frac{11}{4}\\qquad\\textbf{(C)}\\ 2\\sqrt{2}\\qquad\\textbf{(D)}\\ \\frac{17}{6}\\qquad\\textbf{(E)}\\ 3$", "description_html": "<p>In  <span class=\"katex--inline\">\\triangle ABC</span> ,  <span class=\"katex--inline\">AB=6</span> ,  <span class=\"katex--inline\">AC=8</span> ,  <span class=\"katex--inline\">BC=10</span> , and  <span class=\"katex--inline\">D</span>  is the midpoint of  <span class=\"katex--inline\">\\overline{BC}</span> . What is the sum of the radii of the circles inscribed in  <span class=\"katex--inline\">\\triangle ADB</span>  and  <span class=\"katex--inline\">\\triangle ADC</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\sqrt{5}\\qquad\\textbf{(B)}\\ \\frac{11}{4}\\qquad\\textbf{(C)}\\ 2\\sqrt{2}\\qquad\\textbf{(D)}\\ \\frac{17}{6}\\qquad\\textbf{(E)}\\ 3</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": "2017 AMC 10B Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/17_amc10B_p22", "prev": "/problem/17_amc10B_p20"}}