Multiple choice

If PT is a tangent and AB is a chord of circle and they intersect at the point P externally and (2PT = AP)( and ) (AB = 18) units, then PT is equal to

  1. 6 units

  2. 9 units

  3. 12 units

  4. 15 units

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

By the power of a point theorem: PT² = PA × PB. Given 2PT = AP and AB = 18, let PT = x, then AP = 2x. PB = AP - AB = 2x - 18. So x² = 2x(2x - 18). Solving: x² = 4x² - 36x → 3x² = 36x → x = 12.