Minor arc BC subtends angles BAC and BDC at points A and D. respectively, on the circumference in the major sector of the circle with centre O. What is the value [in degrees) of (∠ABC + ∠ACB), if ∠BDC = 73°?

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 :

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?

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?

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?