In the given figure, if PA and PB are tangents to the circle with centre O such that ∠APB = 54°, then OBA = ________.

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SSC CGL 2022 Tier-I Official Paper (Held On : 12 Dec 2022 Shift 4)
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  1. 27°
  2. 40°
  3. 30°
  4. 35°

Answer (Detailed Solution Below)

Option 1 : 27°
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SSC CGL Tier 1 2025 Full Test - 01
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Detailed Solution

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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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