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Moderate

Concentric Circle Probability

ACTMAT-1XDJHJ

The figure below is a dartboard consisting of four concentric circles. This board is divided into four parts, labeled A, B, C, and D (where region A is a circle, and regions B, C, and D are rings). The radius of the inner circle is 1 cm, as is the distance between the subsequent rings.

What is the probability that a dart thrown at the dartboard lands in ring C? Assume the dart hits the board, and the dart lands in region A, B, C, or D (the thickness of each circle is negligible).

A

$ {\cfrac { 1 }{ 4 } } $

B

$ {\cfrac { 1 }{ 2 } } $

C

$ {\cfrac { 3 }{ 4 } } $

D

$ {\cfrac { 5 }{ 16 } } $

E

$ {\cfrac { 7 }{ 16 } } $