UI Post-UTME Mathematics 2025 (Model questions) Question 11

Question 11

Circle Theorems

A circle has centre O and radius 5cm. From an external point P, a tangent PT is drawn to touch the circle at T. If OP = 13cm, find the length PT

  1. A.6cm
  2. B.14cm
  3. C.12cm
  4. D.11cm
Show the answer and explanation

Answer: C (12cm)

Explanation

The radius OT is perpendicular to the tangent, so PT² = 13² − 5² = 144 and PT = 12 cm.