To draw a pair of tangents to a circle which are inclined to each other at an angle of 75°, it is required to draw tangents at the end points of those two radii of the circle, the angle between whom is

Question

Question

This question was previously asked in

RRB ALP Previous Paper 2 (Held On: 9 Aug 2018 Shift 2)

Answer 1

Concept:

Radius is perpendicular to the tangent at the point of contact

Sum of all the angles of a Quadrilateral = 360°

Calculation:

F1 AbhishekP Madhuri 23.02.2022 D1

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

∠OAP = ∠OBP = 90° (Radius is perpendicular to the tangent at the point of contact)

Now, In quadrilateral OAPB,

∠APB + ∠OAP + ∠AOB + ∠OBP = 360°

75° + 90° + ∠AOB + 90° = 360°

∠AOB = 105°

Thus, the angle between the two radii, OA and OB is 105°