Read the following SAT test question, then click on a button to select your answer.
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.
Correct Answer: B
Here's Why:
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.
Difficulty: Medium
Question Type: Standard Multiple Choice.
