Circles
Types of exercises: inscribed and central angles, circle circumscribed on a right triangle, tangent to a circle, chord of a circle, tangent segments, incircle and circumcircle.
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Find the distance of the chord from the centre
A chord of a circle of radius 12 cm is 22 cm long. How far from the centre of the circle is the chord?
Compute the radius of the circumscribed circle
A right triangle has legs 30 cm and 72 cm. What is the radius of the circle circumscribed on it?
Find the perimeter of the triangle
The incircle of triangle ABC touches the sides AB, BC and CA at the points K, L and M respectively. |AK| = 8 cm, |BL| = 7 cm, |CM| = 14 cm. What is the perimeter of triangle ABC?
Find the radius of the incircle
A square has a side of 18 cm. What is the radius of the circle inscribed in it?
Compute the length
A circle has radius 84 cm. A tangent from some point touches it, and the segment from that point to the point of contact is 13 cm. How far is that point from the centre?
Give the measure of the angle
A central angle of a circle measures 68 degrees. What is the inscribed angle on the same arc?
Find the radius of the circle
A chord of a circle is 60 cm long and is 40 cm from the centre of the circle. What is the radius of the circle?
Compute the length
The circle circumscribed on a right triangle has a radius of 7.5 cm, and one leg of the triangle is 12 cm. How long is the other leg?
Find the radius of the circle
Two tangents are drawn from a point P to a circle with centre O; they touch the circle at A and B, |∠APB| = 60° and |PA| = 4√3 cm. What is the radius of the circle?
Find the length of the side
The incircle of an equilateral triangle has a radius of 8√3 cm. How long is a side of the triangle?
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