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Mathematics > Standard Multiple Choice

In the figure above, the circle with center and the circle with center are tangent at point . If the circles each have radius , and if line is tangent to the circle with center at point , what is the value of ?

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### Explanation

The circles each have radius , so . Since the circles are tangent at point , segment contains and . Also, and are perpendicular because a line tangent to a circle forms a right angle with the radius at the point of tangency. Therefore, is a right triangle with hypotenuse and side of length . A right triangle with one side of length one-half that of its hypotenuse is a triangle. The angle is opposite side , so .

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