Circle theorems and constructions

Question 1 of 10

A chord of length 24 cm is in a circle of radius 13 cm. Its distance from the centre is

Question 2 of 10

An arc subtends an angle of 140° at the centre of a circle. What angle does it subtend at the circumference?

Question 3 of 10

The angle at the centre of a circle is 110°. The angle at the circumference on the same arc is

Question 4 of 10

To bisect an angle with ruler and compasses, you draw arcs from the vertex and then

Question 5 of 10

A tangent to a circle meets the radius at the point of contact at

Question 6 of 10

The opposite angles of a cyclic quadrilateral add up to

Question 7 of 10

Two circles of radii 5 cm and 3 cm have centres 10 cm apart. The length of the direct common tangent is

Question 8 of 10

A chord of length 16 cm is in a circle of radius 10 cm. How far is the chord from the centre?

Question 9 of 10

Angles in the same segment of a circle are

Question 10 of 10

In a circle, chords AB and CD intersect at X inside the circle. AX = 4, XB = 6, CX = 3. Find XD.