In the given figure, if PA and PB are tangents to the circle with centre O such that ∠APB = 54°, then ∠ OBA = ________.
27°
Given:
PA and PB are tangents to the circle with center O such that ∠APB = 54°
Calculation:
We know that the radius and tangent are perpendicular at their point of contact.
So,
∠PAO = ∠PBO = 90°
So,
∠AOB = 360 - 54 - 180
⇒ 126°
Also AO = OB = Radius
So, ∠OAB = ∠OBA = 54/2
⇒ 27°
∴ The required answer is 27°
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