Multiple choice

O is the centre of a circle with diameter 20cm. T is a point outside the circle and TA is a tangent to a circle. If OT is 26cm, what is the length (in cm ) of the tangent TA?

  1. 20

  2. 26

  3. 24

  4. 18

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

For a tangent to a circle from an external point, the tangent is perpendicular to the radius at the point of contact. Using the tangent-secant theorem: TA² = OT² - OA². Given OT = 26 cm and OA = radius = 10 cm (diameter = 20 cm), we get TA² = 26² - 10² = 676 - 100 = 576. Therefore, TA = 24 cm. Option C is correct.