SAT Math Multiple Choice Question 620: Answer and Explanation
Note: Figure not drawn to scale.
In the figure above, P is the center of a circle and AC is its diameter. What is the value of x?
- A. 60
- B. 50
- C. 40
- D. 30
Correct Answer: C
Additional Topics (circles and triangles) MEDIUM
Since PA and PB are both radii of the circle, they are congruent, and so triangle APB is isosceles. By the Isosceles Triangle Theorem, then, angle A must also be 20°. From here, you might simply notice that the angle we're looking for, CPB, is the external angle to this triangle, and so it has a measure equal to the sum of the two remote interior angles: 20° + 20° = 40°. Alternately, you could notice that angle APB must have a measure of 140° (since all angles in a triangle have a sum of 180°), and since AC is a straight line, angle CPB = 180° - 140° = 40°.