O is the centre of a circle of radius 10 cm. P is a point outside the circle and PQ is a tangent to the circle. What is the length (in cm) of PQ if the length OP is 26 cm?
Answer & explanation
Correct answer: option 4
According to the question
\( {PQ }^{2 } \) = \( {OP }^{2 } \) + \( {OQ }^{2 } \)
⇒ \( {PQ }^{2 } \) = \( {26 }^{2 } \) + \( {10 }^{2 } \)
⇒ \( {PQ }^{2 } \) = 676 - 100
⇒ \( {PQ }^{2 } \) = 576
⇒ PQ = 24 cm
The length of PQ is 24 cm.