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Radius of Circle

Source: 1968 AHSME Problem #12

September 7, 2011
ratiogeometrycircumcirclearea of a triangleHeron's formulaAMC

Problem Statement

A circle passes through the vertices of a triangle with side-lengths of 712,10,12127\tfrac{1}{2},10,12\tfrac{1}{2}. The radius of the circle is:
<spanclass=′latex−bold′>(A)</span> 154<spanclass=′latex−bold′>(B)</span> 5<spanclass=′latex−bold′>(C)</span> 254<spanclass=′latex−bold′>(D)</span> 354<spanclass=′latex−bold′>(E)</span> 1522<span class='latex-bold'>(A)</span>\ \dfrac{15}{4} \qquad <span class='latex-bold'>(B)</span>\ 5 \qquad <span class='latex-bold'>(C)</span>\ \dfrac{25}{4} \qquad <span class='latex-bold'>(D)</span>\ \dfrac{35}{4} \qquad <span class='latex-bold'>(E)</span>\ \dfrac{15\sqrt2}{2}
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