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Find the length of the arc of a circle of radius 7 cm which subtends an angle of 90 degrees at the center.
If the sum of the radii of two circles which touch each other externally is 10 cm and the distance between their centers is 10 cm, how many common tangents do they have?
An equilateral triangle ABC is inscribed in a circle. What is the angle subtended by side AB at the center?
The difference between the circumference and the radius of a circle is 37 cm. What is its radius?
Find the angle subtended by a chord of length equal to the radius at the center.
A point P is 25 cm from the center of a circle and the length of the tangent from P is 24 cm. The radius of the circle is:
In a cyclic quadrilateral, if the ratio of two opposite angles is 4:5, find the larger angle.
If two circles of radii 18 cm and 8 cm touch each other externally, find the length of their direct common tangent.
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.