Question : O is the centre of this circle. Tangent drawn from a point P, touches the circle at Q. If PQ = 24 cm and OQ = 10 cm, then what is the value of OP?
Option 1: 26 cm
Option 2: 52 cm
Option 3: 13 cm
Option 4: 15 cm
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Correct Answer: 26 cm
Solution :
Given, PQ is a tangent, PQ = 24 cm and OQ = 10 cm
Since tangent is perpendicular to the radius at its point of contact, $\angle$OQP = 90$^\circ$
Using Pythagoras theorem,
OP
2
= PQ
2
+ OQ
2
⇒ OP
2
= 24
2
+ 10
2
⇒ OP
2
= 676
⇒ OP = 26 cm
Hence, the correct answer is 26 cm.
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