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Mathematics > Standard Multiple Choice

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In the figure above, the circle with center A and the circle with center C are tangent at point D. If the circles each have radius 10, and if line l is tangent to the circle with center A at point B, what is the value of x?

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The circles each have radius 10, so A B = A D = D C = 10. Since the circles are tangent at point D, segment Line AC contains D and A C = 20. Also, line A B and l are perpendicular because a line tangent to a circle forms a right angle with the radius at the point of tangency. Therefore, triangle A B C is a right triangle with hypotenuse 20 and side line A B of length 10. A right triangle with one side of length one-half that of its hypotenuse is a 30 degree - 60 degree - 90 degree triangle. The 30 degree angle is opposite side line A B, so x = 90 minus 30 = 60.

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