Question

If tangents PA and PB from a point P to a circle with centre O are inclined to each other at an angle of 130º, then ∠ AOB is

Answer 1

Answer:

50°

Step-by-step explanation:

APB + AOB = 180

130 + AOB = 180

AOB = 180 - 130

= 50°

Answer 2

Answer:

In a OPA and OPB

OP=OP (common)

Angle PAO =Angle PBO (90°each )

OA=OB (equal radii)

By RHS criteria

OPA≈ OPB

therefore Angle 1 = Angle 2 (By C. P. C. T)

Angle 1 = Angle 2 = 1/2 of 80

Angle 1 = Angle 2 = 40°

Now , In POA, By ASP

40°+ Angle POA + 90° = 180°

130°+ Angle POA +90°= 180°

Angle POA =180°-130°

Angle POA = 50°

OPTION (A) IS CORRECT :- 50°