If O is centre of a circle and Chord PQ makes an angle 50° with the tangent PR at the point of contactP, then the angle subtended by the chord at the centre is

The angle subtended by the chord at the centre is 100°.

Here's the step by step solution:

1. In the given question, it is stated that chord PQ makes an angle of 50° with the tangent PR at the point of contact P.

2. According to the properties of a circle, the angle between a tangent and a chord through the point of contact is equal to the angle subtended by the chord in the alternate segment.

3. Therefore, the angle subtended by chord PQ in the alternate segment (which is the angle subtended at the centre O) is also 50°.

4. However, the angle subtended by a chord at the centre is twice the angle subtended by it at any point on the alternate segment of the circle.

5. Therefore, the angle subtended by chord PQ at the centre O is 2 * 50° = 100°.