Multiple choice

A point P is $26 cm$ away from the centre O of a circle and the length PT of tangent drawn from P to the circle is $10 cm$. Then the radius of the circle is

  1. $18 cm$
  2. $20 cm$
  3. $22 cm$
  4. $24 cm$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A tangent to a circle is perpendicular to the radius at the point of contact. This forms a right-angled triangle with the hypotenuse as the distance from the center to the external point (26 cm) and one leg as the tangent (10 cm). Using the Pythagorean theorem, r^2 + 10^2 = 26^2, so r^2 = 676 - 100 = 576, giving r = 24 cm.

AI explanation

The radius is perpendicular to the tangent at the point of contact, so triangle OPT is a right-angled triangle with OP as the hypotenuse. Applying the Pythagorean theorem, the radius OT squared equals OP squared minus PT squared, which is 26 squared minus 10 squared. Calculating 676 minus 100 gives 576, and the square root of 576 is 24 cm.

Keep practicing — related questions