MathDB
2018 Individual #24

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January 13, 2023
2018 Individual

Problem Statement

The sides of △ABC\triangle ABC form an arithmetic sequence of integers. Incircle II is tangent to ABAB, BCBC, and CACA at DD, EE, and FF, respectively. Given that DB=32DB = \tfrac32, FA=12FA = \tfrac12, find the radius of II.
<spanclass=′latex−bold′>(A)</span>12<spanclass=′latex−bold′>(B)</span>157<spanclass=′latex−bold′>(C)</span>156<spanclass=′latex−bold′>(D)</span>2159<spanclass=′latex−bold′>(E)</span>154<span class='latex-bold'>(A) </span> \dfrac12\qquad<span class='latex-bold'>(B) </span> \dfrac{\sqrt{15}}7\qquad<span class='latex-bold'>(C) </span> \dfrac{\sqrt{15}}6\qquad<span class='latex-bold'>(D) </span> \dfrac{2\sqrt{15}}{9}\qquad<span class='latex-bold'>(E) </span> \dfrac{\sqrt{15}}{4}
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