Question

The angle between two radii OA and OB of a circle is 130°. Then the
angle between the two tangents drawn at the points A and B is​

Answer 1

Step-by-step explanation:

PA and PB are tangents drawn from an external point P to the circle.

∠OAP=∠OBP=90

∘

(Radius is perpendicular to the tangent at point of contact)

In quadrilateral OAPB,

∠APB+∠OAB+∠AOB+∠OBP=360

∘

35

∘

+90

∘

+∠AOB+90

∘

=360

∘

215

∘

+∠AOB = 360

∘

∠AOB=360

∘

–280

∘

=145

∘

Thus, the angle between the two radii, OA and OB is 145

∘

.