if o is centre of a circle and chord pq makes an angle 50° with the tangent pr at the point of contact p, then the angle subtended by the chord at the centre is
If o is the centre of a circle and chord pq makes an angle 50° with the tangent pr at the point of contact p, what is the angle subtended by the chord at the centre?
Answer:
In this case, we have a circle with center O and a chord PQ that makes a 50° angle with the tangent PR at the point of contact P. To find the angle subtended by the chord at the center of the circle, we can use the theorem that states “the angle subtended by a chord at the center of a circle is twice the angle subtended by it at any point on the circumference.”
Given that angle PRQ is 90° (angle between the tangent and the radius at the point of contact is always 90°), we can deduce that angle POQ (the angle subtended by the chord at the center) is twice angle PRQ. Therefore, angle POQ = 2 * 50° = 100°.
So, the angle subtended by the chord PQ at the center of the circle is 100°.