Question 38
Circle TheoremsIn the diagram, PQ is the tangent to the circle RST at T. |ST| = SR and ∠RTQ = 68°. Find ∠PTS.
- A.68°
- B.62°
- C.61°
- D.56°
- E.34°
Show the answer and explanation
Answer: D (56°)
Explanation
By the alternate segment theorem, ∠TSR = ∠RTQ = 68°. Triangle STR is isosceles, so ∠STR = (180° − 68°)/2 = 56°. Then ∠PTS = 180° − 68° − 56° = 56°.