Circle theorems and constructions

Question 1 of 10

Two tangents are drawn to a circle from an external point. The two tangent lengths are

Question 2 of 10

ABCD is a cyclic quadrilateral with ∠ABC = 110° and ∠BAD = 75°. Find ∠ADC.

Question 3 of 10

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

Question 4 of 10

The opposite angles of a cyclic quadrilateral add up to

Question 5 of 10

A chord is 6 cm from the centre of a circle of radius 10 cm. Its length is

Question 6 of 10

To construct an angle of 60° with a ruler and compasses, you construct

Question 7 of 10

A tangent from a point 13 cm from the centre of a circle of radius 5 cm has length

Question 8 of 10

Angles in the same segment of a circle are

Question 9 of 10

To construct an angle of 45°, you

Question 10 of 10

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