The angle subtended at the centre of a circle by an arc of the circle measures 128.5^°. Find the angle subtended at the circumference of the circle by the same arc.

PQ is a chord in the minor segment of a circle and R is a point on the minor arc PQ. The tangents at the points P and Q meet at the point T. If ∠PRQ =102°, then the measure of ∠PTQ is :

In a circle, a chord AB is 12 cm long and is at a distance of 4 cm from the center. What is the radius of the circle?

Two chords AB and CD intersect at a point P inside a circle. If AP = 6 cm, PB = 8 cm, and CP = 4 cm, what is the length of PD?

A chord of a circle has a length of 12 cm. The angle subtended by the chord at a point on the circumference is 30°. What is the distance from the center of the circle to the chord?

There are two parallel chords measuring 16 cm and 12 cm, both situated on the same side of the center of a circle. The space between the two chords is 2 cm. What is the radius of the circle?

What is the area of the segment formed by a chord in a circle of radius 12 cm, if the angle subtended at the center is 150°?

In a circle, the length of a chord is 12 cm and the perpendicular distance from the centre of the circle to the chord is 5 cm. What is the radius of the circle? (Rounded up to two decimal places.)​

What is the ratio of the angles subtended by a chord at the centre of a circle to the angle subtended at any point on the circumference of the circle?

In a circle, two chords, AB and CD, measuring 14 cm and 6 cm, respectively, are parallel to each other on the same side of the centre. If the distance between them is 4 cm, find the length (in cm) of the diameter of the circle.​

POR is the diameter of a circle. PQ and RQ are its two chords. The length of arc $$\overline{PQ}$$ is half of the length of are $$\overline{RQ}$$. Find the measure of ∠POQ.​