Question

The length of tangent from a point Q to a circle is 24 cm and the distance of Q from the centre of circle is 25 cm. Then radius of the circle will be

• A. 7 cm
• B. 12 cm
• C. 15 cm
• D. 24.5 cm

Hint:

In a circle, if a tangent of length $l$ is drawn from a point at a distance $d$ from the centre, then radius $r = \sqrt{d^2 - l^2}$.

Answer 1

The Correct Option is A

Step 1: Use the property of tangents.
For a point $Q$ outside a circle, if $QT$ is the tangent and $OQ$ is the line joining the centre to the point, then \[ OQ^2 = OT^2 + QT^2 \] where $OT = r$ (radius) and $QT$ is the tangent length.
Step 2: Substitute given values.
Given $QT = 24$ cm, $OQ = 25$ cm.
\[ 25^2 = r^2 + 24^2 \] \[ 625 = r^2 + 576 \] \[ r^2 = 625 - 576 = 49 \] \[ r = 7 \, \text{cm} \] Step 3: Conclusion.
Hence, the radius of the circle is 7 cm.