Question

In the given figure, O is the centre of a circle, AB is a chord and AT is the tangent at A. If ∠AOB = 100° then ∠BAT is equal to ______.

Options

• 40°

• 50°

• 90°

• 100°

Answer 1

In the given figure, O is the centre of a circle, AB is a chord and AT is the tangent at A. If ∠AOB = 100° then ∠BAT is equal to 50°.

Explanation:

Mark a point C in the alternate segment. Join AC and BС.

`∠ACB = 1/2 ∠AOB = 1/2 xx 100^circ = 50^circ`   ...[∵ Angle at the centre is double the angle on the circle]

Now, ∠BAT = ∠ACB = 50°   ...[Angles in alternate segments]