A) \[\frac{R}{2}\]
B) \[\frac{R}{\sqrt{3}}\]
C) \[\frac{2\sqrt{R}-\sqrt{R}}{\sqrt{2}}\]
D) \[R\left( 1-\frac{1}{\sqrt{3}} \right)\]
Correct Answer: D
Solution :
[d] From similar triangles, \[\frac{QC}{\sin 30{}^\circ }=\frac{R}{\sin 120{}^\circ }\] or \[QC=R\times \frac{\sin 30{}^\circ }{\sin 120{}^\circ }=\frac{R}{\sqrt{3}}\] Thus \[PQ=PC-QC=R-\frac{R}{\sqrt{3}}=R\left( 1-\frac{1}{\sqrt{3}} \right)\]You need to login to perform this action.
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