In a circle, two chords of lengths x and y subtend the angles of 60° and 90° at the center respectively. Which of the following is correct in this scenario?

Correct option is A

Given:

- Two chords in a circle with lengths x and y.

- Chord of length x subtends an angle of 60° at the center.

- Chord of length y subtends an angle of 90° at the center.

Solution: 

Let the radius of the circle be r 

Length of chord a = r      ....(1)        (all angles are 60°)

Length of chord b = r√2      ....(2)          (chord b is making an isosceles right angle   triangle)

From equation 1 and 2 

b = a√2