Transcript Difficulty: Medium In the figure above, the circle with center A and the circle with center C are tangent at point D.

Difficulty: Medium
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 is tangent to
the circle with center A at point B, what is the value
of x?
a) 55
b) 60
c) 63
d) 65
e) It cannot be determined from the information given.
HINT
The measure of ABC is 90° because a line tangent to a circle is perpendicular
to the radius of the circle that contains the point of tangency. This means that
 ABC is a right triangle.
B: 60
Explanation:
The circles each have radius 10, so AB = AD = DC = 10. Since the circles are
tangent at point D, segment
contains D and AC = 20. Also,
and are
perpendicular because a line tangent to a circle forms a right angle with the
radius at the point of tangency. Therefore, ABC is a right triangle with
hypotenuse 20 and side
of length 10. A right triangle with one side of length
one-half that of its hypotenuse is a 30° - 60° - 90° triangle. The 30° angle is
opposite side , so x = 90 – 30 = 60.