Question

In the given figure, RQ is a tangent to the circle with centre O, If SQ = 6 cm and QR = 4 cm. then OR is equal to

(a) 2.5 cm 

(b) 3 cm 

(c) 5 cm 

(d) 8 cm

Answer 1

Correct answer is (c) 5 cm

We know that the radius and tangent are perpendicular at their point of contact

\(OQ=\frac{1}{2}QS=3cm\)   [∵ Radius is half of diameter]

Now, in right triangle OQR 

By using Pythagoras theorem, we have

OR² = RQ² + OQ²

= 4² + 3²

= 16 + 9

= 25

∴ OR² = 25

\(\Rightarrow\) OR = 5 cm