Choose the correct option:

A circle has radius $\sqrt{2}$ cm.  It is divided into two segments by a chord of length 2 cm. Then, the angle subtended by the chord at a point in the major segment is ________.

According to the question, let us draw a figure.

From the figure, 

BC² = (2)² = 4 cm

And,

OB² + OC² = (√2)² + (√2)² = 2 + 2 = 4 cm

So, we can say that BC² = OB² + OC²

∴ ∠BOC = 90^o    [By converse of Pythagoras theorem]

We know that the angle subtended by the chord at the centre is double the angle subtended by it at any point on the circle.

∴ ∠BAC = $\frac{1}{2}$∠BOC = $\frac{1}{2}\times {90}^0={\mathbf{45}}^{\mathbf{o}}$

Hence, the angle subtended by the chord at a point in the major segment is 45^o.