Multiple choice

The length of tangent drawn from an external point P to a circle with centre O, is 8 cm. If the radius of the circle is 6 cm, then the length of OP (in cm) is :

  1. $2\sqrt{7}$
  2. $4\sqrt{7}$

  3. 10

  4. 10.5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The radius, tangent, and the line from the center to the external point form a right-angled triangle where the hypotenuse is OP. By Pythagoras theorem, OP^2 = 8^2 + 6^2 = 64 + 36 = 100, so OP = 10.

AI explanation

The tangent to a circle is perpendicular to the radius at the point of contact, forming a right-angled triangle where OP is the hypotenuse. Applying the Pythagorean theorem gives OP squared equals 6 squared plus 8 squared, which equals 36 plus 64. The sum is 100, so OP equals 10 cm.

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