MathDB
Four Circles

Source: 2015 AMC 12B # 24

February 26, 2015
Pythagorean Theoremgeometryperpendicular bisectorAMC

Problem Statement

Four circles, no two of which are congruent, have centers at AA, BB, CC, and DD, and points PP and QQ lie on all four circles. The radius of circle AA is 58\frac{5}{8} times the radius of circle BB, and the radius of circle CC is 58\frac{5}{8} times the radius of circle DD. Furthermore, AB=CD=39AB = CD = 39 and PQ=48PQ = 48. Let RR be the midpoint of PQ‾\overline{PQ}. What is AR+BR+CR+DRAR+BR+CR+DR?
<spanclass=′latex−bold′>(A)</span> 180<spanclass=′latex−bold′>(B)</span> 184<spanclass=′latex−bold′>(C)</span> 188<spanclass=′latex−bold′>(D)</span> 192<spanclass=′latex−bold′>(E)</span> 196 <span class='latex-bold'>(A)</span>\ 180 \qquad<span class='latex-bold'>(B)</span>\ 184 \qquad<span class='latex-bold'>(C)</span>\ 188 \qquad<span class='latex-bold'>(D)</span>\ 192\qquad<span class='latex-bold'>(E)</span>\ 196
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