If the angle between two radii of a circle be 130^\circ, then the angle between the tangents at the end of these radii (in degrees) is

SSC CHSL 19 Mar 2020 Shift 3 Paper

Question : 67 of 100

Marks: +1, -0

If the angle between two radii of a circle be

130°

, then the angle between the tangents at the end of these radii (in degrees) is

Solution:

Given,

\∠\AOB=130°

Since, PA and PB are tangents,
∴

\∠\OAP=90°

and

\∠\OBP=90°

In quadrilateral OAPB,

\∠\OAP+\∠\AOB+\∠\OBP+\∠\APB=360°

90°+130°+90°+\∠\APB=360°

\∠\APB=360°-(90°+90°+130°)

=360°-310°=50°

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