Question

O is the centre of a circle of radius 6 cm. P is the point such that AP = 10 cm and OP intersects the circle at T and PC, PD are two tangents drawn to the circle. if AB is the tangent to the circle at T find the length AB.​

Answer 1

Step-by-step explanation:

Let O be the centre of the given circle and let P be a point such that OP = 10 cm.

Let PT be the tangent such that PT = 8 cm.

Join OT.

Now, PT is a tangent at T and OT is the radius through T.

Therefore, OT⊥PT.

Using pythagoras theorem in △OTP, we have,

OP

2

=OT

2

+PT

2

OT

2

=100−64=36

OT=6 cm

Therefore, the radius of the circle is 6 cm.