AB is the diameter of a circle with centre O. P be a point on it. If ∠AOP = 95°, then ∠OBP __________.

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SSC CGL 2023 Tier-I Official Paper (Held On: 14 Jul 2023 Shift 3)
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  1. 57.5°
  2. 45.5°
  3. 47.5°
  4. 55.5°

Answer (Detailed Solution Below)

Option 3 : 47.5°
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PYST 1:SSC CGL 2023 - Quantitative Aptitude(Held On:14 Jul 2023 Shift 1)
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Detailed Solution

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Given :

AB is a diameter of circle centre O,

Formula used : 

Linear pair angle,  angle on straight line = 180°

Calculation

F3 SSC Savita 09-10-23 D9

∠AOP = 95 °

∠POB = ( 180 ° - 95 °) = 85°

∆ POB = ∠P = ∠B ( Isosceles  triangle )

⇒ ∠POB = 85° 

∆ POB = ∠POB + ∠ OBP + ∠ BPO = 180°

⇒ 180° = 85°+ 2 × ∠OBP

⇒ 95/2 = ∠OBP

⇒ 47.5°  =  ∠OBP 

The value of ∠OBP is 47.5°.

Shortcut Trick∠OBP = 1/2 × of ∠AOP

∠OBP = 1/2 × of 95 = 47.5

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