Correct option is B
Given:
OA, OB, and OC are radii of a quarter circle → ∠AOC = 90°
AB = radius
Triangle OAB is equilateral because OA = OB = AB (all equal to radius)
We are to find angle ∠OCB
Concept Used:
Use triangle properties:
Equilateral triangle => all angles = 60°
Use triangle and angle subtraction to find unknowns
Solution:
Step 1: Triangle OAB is equilateral
→ So, all angles = 60°
→ ∠AOB = 60°
Step 2: In triangle COB:
∠AOC = 90° (quarter circle)
→ So, ∠BOC = 90° – ∠AOB = 90° – 60° = 30°
Step 3: Triangle OCB is isosceles (OC = OB)
Angle ∠OCB = angle ∠OBC
Let each of these equal x
So, total angles in triangle OCB = x + x + 30° = 180°
→ 2x = 150°
→ x = 75°
Correct Option: (B) 75°
