Circles

In a cyclic quadrilateral ABCD, if angle A = 3x and angle C = x, find the value of x.

The lengths of two parallel chords of a circle are 6 cm and 8 cm. If the radius is 5 cm, and chords are on the same side of the center, find the distance between them.

If the angle between two radii is 120 degrees, find the angle between the tangents at the ends of those radii.

Find the area of a sector of a circle with radius 6 cm if the angle of the sector is 60 degrees.

If a square is inscribed in a circle of radius r, what is the area of the square?

What is the angle subtended by a minor arc in the major segment?

In the figure, PQ is a tangent at P. If O is the center and angle OPQ = 90 degrees, and OP = 5 cm, OQ = 13 cm, find PQ.

Two circles touch internally. Their radii are 10 cm and 4 cm. What is the distance between their centers?

Angle in the major segment of a circle is:

The length of a tangent from a point 10 cm away from the center of a circle of radius 6 cm is:

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

Find the area of the largest triangle that can be inscribed in a semi-circle of radius r.

A chord of length 24 cm is at a distance of 5 cm from the center. Find the radius.

How many common tangents do two circles have if they intersect at two points?

If the circumference of a circle is equal to the perimeter of a square, then the ratio of their areas is:

An arc of length 15 cm subtends an angle of 45 degrees at the center. Find the radius.

Find the angle subtended at the center by a chord which is equal to the radius.

If a chord is 16 cm long and the radius of the circle is 10 cm, how far is the chord from the center?

If a cyclic quadrilateral has one angle equal to 70 degrees, what is the measure of the opposite angle?

In a circle, a chord AB is 10 cm and the radius is 13 cm. What is the distance of the chord from the center?