Circles

If the circumference of a circle and the perimeter of a square are equal, which has the larger area?

If a chord subtends an angle of 120 degrees at the center of a circle of radius 12 cm, find the length of the chord.

In a circle with center O, PT is a tangent and PAB is a secant. If PT = 6 cm and AB = 5 cm, find PA.

Find the length of the direct common tangent to two circles of radii 12 cm and 7 cm, if the distance between their centers is 13 cm.

What is the area of a sector whose arc length is 10 cm and radius is 5 cm?

If a circle is circumscribed about a right-angled triangle with legs 6 cm and 8 cm, find its radius.

The area of a circle inscribed in a square of side 10 cm is:

In a circle, the distance between two parallel chords of length 6 cm and 8 cm is 1 cm. What is the radius?

If the ratio of the areas of two circles is 4:9, what is the ratio of their circumferences?

A wire is in the form of a circle of radius 42 cm. It is bent into a square. Find the side of the square.

If the sector of a circle of radius 6 cm has an angle of 120 degrees, find the perimeter of the sector.

The difference between the circumference and radius of a circle is 37 cm. Find the area.

Two concentric circles have radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

If an equilateral triangle is inscribed in a circle of radius r, what is the side of the triangle?

The area of a circle is decreased by 19% if its radius is decreased by what percent?

Find the area of the ring between two concentric circles whose circumferences are 88 cm and 66 cm.

If the length of a transverse common tangent to two circles is 8 cm and the radii are 5 cm and 1 cm, find the distance between centers.

A square is circumscribed about a circle. What is the ratio of the area of the square to the area of the circle?

In a cyclic quadrilateral, if the ratio of three consecutive angles is 1:2:3, find the fourth angle.

The area of a circle that can be inscribed in a square of side 6 cm is: