Question

The two tangents from an external point S to a circle with centre O are SA and SB. If ∠ASB = 50°,
find the value of ∠ AOB.

Answer 1

Given : The two tangents from an external point S to a circle with centre O are SA and SB.

ASB = 50°

To Find : ∠ AOB.

Solution:

in Quadrilateral  OASB

∠OAS + ∠ASB + ∠OBS  + ∠AOB = 360°

∠OAS  =∠OBS   = 90°   as   SA and SB are tangents

∠ASB  = 50°

=> 90°  + 50°  + 90°   + ∠AOB = 360°

=> 230°   + ∠AOB = 360°

=>  ∠AOB = 130°

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