Question

A point A is 26 cm away from the center of a circle and the length of tangent drawn from A to the circle is 24 cm. Find the radius of the circle.

• A. 10
• B. 2 $\sqrt{313}$
• C. 7
• D. 12

Answer 1

The correct option is A

10

Let O be the center of the circle and let A be a point outside the circle such that OA = 26 cm.

Let AT be the tangent to the circle.

Then, AT = 24 cm. Join OT.

Since the radius through the point of contact is perpendicular to the tangent, we have $\angle$OTA = 90°. In right $△$ OTA, we have

${OT}^2$ = ${OA}^2$ – ${AT}^2$

= [ ${\left(26\right)}^2$ – ${\left(24\right)}^2$] = (26 + 24) (26 – 24) = 100.

=> OT =$\sqrt{100}$ = 10 cm.

Hence, the radius of the circle is 10 cm.