Question

The tangent PQ of a circle of radius 5 cm meets at a point Q on the line passing through the centre O. If OQ = 12 cm, then the measure of PQ will be

• A. 12 cm
• B. 13 cm
• C. 8.5 cm
• D. $\sqrt{119}$ cm

Hint:

When a tangent and radius meet, they form a right angle. Use the Pythagoras theorem in such tangent problems.

Answer 1

The Correct Option is D

Step 1: Identify the given data. 
Radius \( r = 5 \) cm, \( OQ = 12 \) cm. We have to find \( PQ \). 
Step 2: Use the property of tangent and radius. 
The radius drawn to the tangent at the point of contact is perpendicular to the tangent. Thus, \( \triangle OPQ \) is a right-angled triangle at \( P \). 
Step 3: Apply the Pythagoras theorem. 
\[ OQ^2 = OP^2 + PQ^2 \] \[ PQ^2 = OQ^2 - OP^2 = 12^2 - 5^2 = 144 - 25 = 119 \] \[ PQ = \sqrt{119} \text{ cm} \] Step 4: Conclusion. 
Hence, the length of the tangent \( PQ = \sqrt{119} \) cm.