Question

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

पर्याय

• `2sqrt313`

• 12

• 7

• 10

Answer 1

10

Explanation:

Let O be the centre 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 ∠OTA = 90°. In right ΔOTA, we have 

OT² = OA² - AT²

= [(26)² - (24)²] = (26 + 24) (26 - 24) = 100.

⇒ OT = `sqrt100` = 10 cm

Hence, the radius of the circle is 10 cm.