Question 31
Circle TheoremsIn the figure above, TZ is tangent of the circle QPZ. Find x if TZ = 6 units and PQ = 9 units.
- A.3
- B.4
- C.5
- D.6
Show the answer and explanation
Answer: A (3)
Explanation
Tangent–secant rule: TZ² = TP × TQ, so 36 = x(x + 9). Then x² + 9x − 36 = 0, (x + 12)(x − 3) = 0 and x = 3.