Define the "angle subtended by an arc at the centre" and the "angle subtended by the same arc on the remaining part of the circle".

State the theorem that relates the angle at the centre and the angle on the circumference subtended by the same arc.

An arc AB of a circle with centre O subtends an angle AO^B=100∘ at the centre. What is the magnitude of the angle AC^B where C is a point on the major arc?

State the theorem about angles in the same segment of a circle.

In a circle, points P, Q, R, and S are on the circumference. If PR^Q=30∘, what is the magnitude of PS^Q?

What is an "angle in a semicircle"?

State the theorem regarding the angle in a semicircle.

PQ is a diameter of a circle with centre O. R is a point on the circumference. What is the magnitude of PR^Q?

In a circle with centre O, A, B, and C are points on the circle. If OA^B=20∘ and OC^B=30∘, find the magnitude of the reflex angle AO^C.

A, B, C and D are points on a circle. If CA^D=50∘ and CB^D=x, find the value of x.

PQ is a diameter of the circle PQRS. If QP^R=20∘ and PS = QR, find the magnitude of RP^S.

The points P, Q, R, and S lie on a circle. Prove that PQ^​S+SR^P=QP^R+RS^Q.

The points A, B, and C lie on a circle with centre O. Prove that AO^B=2×OC^A+2×OC^B.

AC is a diameter of the circle ABCD. If BC is parallel to AD, prove that ABCD is a rectangle.

Two circles intersect at points P and Q. PX and PY are diameters of the two circles. Show that the points X, Q, and Y are collinear (lie on a straight line).