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Question:

A tangent PQ at a point P of a circle of radius 5cm meets a line through the centre O at a point Q so that OQ=12cm. Length PQ is:

8.5cm

√119cm

12cm

13cm

Solution:

The correct option is B √119cm
OP=5cm and OQ=12cm
To find: PQ
By using Pythagoras Theorem, we have
OP² + PQ² = OQ²
Putting given values in above equation
5² + PQ² = 12²
⟹ PQ² = 144 - 25
⟹ PQ² = 119
PQ = √119cm