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P21 [Geometry] - Turkish NMO 1st Round - 2002

Source:

August 10, 2014
geometrycircumcircletrigonometrytrapezoid

Problem Statement

Let A1A2⋯A10A_1A_2 \cdots A_{10} be a regular decagon such that [A1A4]=b[A_1A_4]=b and the length of the circumradius is RR. What is the length of a side of the decagon?
<spanclass=′latex−bold′>a)</span> b−R<spanclass=′latex−bold′>b)</span> b2−R2<spanclass=′latex−bold′>c)</span> R+b2<spanclass=′latex−bold′>d)</span> b−2R<spanclass=′latex−bold′>e)</span> 2b−3R <span class='latex-bold'>a)</span>\ b-R \qquad<span class='latex-bold'>b)</span>\ b^2-R^2 \qquad<span class='latex-bold'>c)</span>\ R+\dfrac b2 \qquad<span class='latex-bold'>d)</span>\ b-2R \qquad<span class='latex-bold'>e)</span>\ 2b-3R
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