If the tangent at a point P to a circle with centre O cuts a line through O at Q such that PQ = 24 cm and OQ = 25 cm. Find the radius of the circle.

Given: PQ = 24 cm

OQ = 25 cm

To find: The value of OT.

Theorem Used:

1.) A tangent to a circle is perpendicular to the radius through the point of contact.

2.) Pythagoras theorem:

In a right-angled triangle, the squares of the hypotenuse is equal to the sum of the squares of the other two sides.

Explanation:

Since QT is a tangent to the circle at T and OT is radius,

Therefore, by the theorem stated, OT perpendicular QT

In ΔOTQ,

By Pythagoras theorem we have

OQ² = OT² + TQ²

For the given values,

⇒ OT² = 25² – 24²

⇒ OT² = 625 – 576

⇒ OT² = 49

⇒ OT = √49

⇒ OT=7 cm