In a circle with centre $O$, a chord $AB$ subtends an angle of $60^{\circ }$ at the centre. A tangent at point $A$ meets the extension of chord $AB$ at point $T$. What is the measure of $\angle TBA$?

Step-by-step solution

1. Recall that the angle between a tangent and a chord equals the angle in the alternate segment of the circle.
2. The chord $AB$ subtends $60^{\circ }$ at the centre, so it subtends half of that, i.e. $30^{\circ }$, at any point on the circle in the opposite segment.
3. Therefore $\angle TBA=30^{\circ }$.

Concept tested: Angle between tangent and chord

Published 20 August 2026 · Last updated 16 September 2026 · How this solution was prepared and checked