Question

33. If PA and PB are two tangents to a circle
with center O, from a point P outside the
circle, such that < OPB = 40, then < AOP =
(1 Point)
600
50°
40°​

Answer 1

Step-by-step explanation:

If two tangents inclined at an angle 60° are drawn to a circle of radius 3 cm, then the length of each tangent is equal to?

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 = 3 cm.

In the right triangle OAP,

OA/AP = tan 30° => 3/AP = 1/√3

So AP= 3√3cm or3×1.732=5.196 cm

So length of each tangent = 5.196 cm.