If a chord AB of a circle subtends an angle `theta(nepi//3)` at a point C on the circumference such that the triangle ABC has maximum area , then

Options

A. `A=pi/3+(theta)/2,B=(2pi)/3-(3theta)/2`
B. `A=(pi)/4+(theta)/2,B=(3pi)/4-(3theta)/2`
C. `A=pi/6+theta,B=(5pi)/6+2theta)`
D. none of these

Explanation

To solve the problem, we need to find the angles A and B of triangle ABC, given that the chord AB subtends an angle θ (which is π/3) at point C on the circumference of the circle, and that the triangle ABC has maximum area.

### Step-by-Step Solution:

1. **Understanding the Geometry**:
- We have a circle with chord AB.
- The angle θ = π/3 is subtended by chord AB at point C on the circumference.
- We need to find angles A and B such that the area of triangle ABC is maximized.
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