Two chords of length a unit and b unit of a circle make angles 60° and 90° at the centre of a circle respectively, then the correct relation is

Length of chord CD = $$a$$ and AB = $$b$$

Let radius of the circle be $$r$$

In $$\triangle$$OAB, by using Pythagoras theorem

=> $$r^2 + r^2 = b^2$$

=> $$2r^2 = b^2$$

=> $$r = \frac{b}{\sqrt{2}}$$ ------Eqn(1)

Now, in $$\triangle$$COD, OC = OD = radii

=> $$\angle$$OCD = $$\angle$$ODC = $$\angle$$COD = 60°

=> OCD is equilateral triangle

=> $$a = r$$ ---------Eqn(2)

From eqns(1) & (2), we get :

$$a = \frac{b}{\sqrt{2}}$$

=> $$b = \sqrt{2}a$$