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Easy Incircles

Source: 2017 AMC 10B #21

February 16, 2017
AMCAMC 10AMC 10 Bgeometry2017 AMC 10B

Problem Statement

In △ABC,\triangle ABC, AB=6,AC=8,BC=10,AB=6, AC=8, BC=10, and DD is the midpoint of BC‾.\overline{BC}. What is the sum of the radii of the circles inscribed in △ADB\triangle ADB and △ADC?\triangle ADC?
<spanclass=′latex−bold′>(A)</span>5<spanclass=′latex−bold′>(B)</span>114<spanclass=′latex−bold′>(C)</span>22<spanclass=′latex−bold′>(D)</span>176<spanclass=′latex−bold′>(E)</span>3<span class='latex-bold'>(A)</span> \sqrt{5} \qquad <span class='latex-bold'>(B)</span> \frac{11}{4}\qquad <span class='latex-bold'>(C)</span> 2\sqrt{2} \qquad <span class='latex-bold'>(D)</span> \frac{17}{6} \qquad <span class='latex-bold'>(E)</span> 3
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