Question

The length of the tangent to a circle with centre O and radius = 6 cm from a point P outside the circle such that OP = 10 cm is 

(A) 6 cm 

(B) 8 cm 

(C) 4 cm 

(D) 5 cm

Answer 1

Correct option is: (B) 8 cm

\(\because \) \(\angle\) OQP = 90° (Angle between tangent & radius at point of contact)

In right \(\triangle \) OQP

\(OP^2 = OQ^2 + PQ^2\)

= \(PQ^2 = OP^2 - OQ^2 = 10^2 - 6^2\)

= 100 -36 = 64.

\(\therefore\) PQ = 8 cm

Hence, the length of tangent to circle from point P is 8 cm.

Answer 2

Correct option is: (B) 8 cm