Circles

The angle between a tangent to a circle and a chord through the point of contact is equal to:

In a circle with center O, chords AB and CD are equal. If angle AOB = 70 degrees, what is angle COD?

If the angle between two radii of a circle is 130 degrees, the angle between the tangents at the ends of the radii is:

A chord is 24 cm long and its distance from the center is 5 cm. What is the radius of the circle?

What is the area of a circle inscribed in a square of side 14 cm?

In a cyclic quadrilateral ABCD, if angle A - angle C = 60 degrees, find angle A.

The angle subtended by a major arc at the center is 250 degrees. What is the angle subtended by the minor arc at the center?

In the figure, PQ and PR are tangents to the circle with center O. If angle QPR = 40 degrees, find angle QOR.

If the length of a chord of a circle of radius 10 cm is 16 cm, find its distance from the center.

In the figure, O is the center and AB is a diameter. C is a point on the circle such that angle ABC = 30 degrees. Find angle BAC.

If the angle between two tangents drawn from an external point P to a circle is 120 degrees and the radius is 10 cm, find the distance of the point P from the center.

A circle is inscribed in a triangle ABC with sides 8 cm, 10 cm, and 12 cm. Find the length of the segment of the side 12 cm from the vertex opposite to the side 10 cm.

Find the area of the segment of a circle of radius 14 cm if the central angle is 90 degrees.

Two circles touch each other externally at point T. A direct common tangent AB touches the circles at A and B. Find the measure of angle ATB.

A chord of a circle is equal to its radius. Find the angle subtended by this chord at a point on the major arc.

In a circle of radius 5 cm, AB and CD are two parallel chords of length 8 cm and 6 cm respectively. If they lie on opposite sides of the center, find the distance between them.

In the figure, O is the center. AB is a chord and PT is the tangent at T. If PT = 12 cm and the distance of P from the center is 13 cm, find the radius.

If a cyclic trapezium has its non-parallel sides equal, what kind of trapezium is it?

In a circle, two chords AB and CD intersect at a point E outside the circle. If AB = 5, BE = 4, and DE = 6, find the length of CD.

The length of the common chord of two intersecting circles is 24 cm. If their radii are 13 cm and 15 cm, find the distance between their centers.