Circles

The area of a sector is 1/12 of the area of the circle. What is the central angle of the sector?

An arc of length 20 cm subtends an angle of 2 radians at the center. What is the radius of the circle?

If the angle between two tangents from P to a circle is 90 degrees and the radius is 5 cm, what is the length of each tangent?

In a cyclic quadrilateral ABCD, side AB is the diameter. If angle ADC = 130 degrees, find angle BAC.

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

If a circle passes through the vertices of a triangle with sides 3, 4, and 5, what is the radius of the circle?

Two circles touch internally. The sum of their areas is 170*pi and the distance between their centers is 4. Find the radius of the larger circle.

In the figure, O is the center. PA and PB are tangents. If angle AOB = 120 degrees, find angle OAB.

What is the angle in a segment greater than a semi-circle?

A square is inscribed in a circle of area 154 sq. cm. Find the area of the square.

The angle between a tangent and its chord is 50 degrees. What is the angle in the alternate segment?

Three circles of radius 1 cm touch each other externally. What is the area of the region enclosed between them?

A circle is inscribed in a right-angled triangle with sides 6, 8, and 10. Find its radius.

If the circumference of a circle is increased from 4*pi to 8*pi, what happens to its area?

In the figure, if chord AB is parallel to tangent at C, then triangle ABC is:

The length of a transverse common tangent to two circles of radii 8 cm and 2 cm with centers 13 cm apart is:

If a rectangle is inscribed in a circle, its diagonal is always the:

How many common tangents can be drawn to two circles that do not intersect and one is not inside the other?

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

What is the locus of the center of a circle which touches a given line at a given point?