Question

if two tangents inclined at an angle of 60 are drawn to a circle of r=6cm then find length of each tangent ​

Answer 1

Answer : length of each tangent is 10.392 cm.

Step-by-step explanation:

Suppose O be the centre of the circle and PA and PB be the two tangents drawn from P to the circle so that angle APB= 60°

Join OP,OA and OB.

Then angle OAP= angle OBP = 90° and

angle OPA = angle OPB = 30°

OA = OB = 6 cm.

In the right triangle OAP,

OA/AP = tan 30° => 6/AP = 1/√3

So AP= 6√3cm or 6×1.732=10.392 cm

So length of each tangent = 10.392 cm.