Core Mathematics

1A tangent from a point 13 cm from the centre of a circle of radius 5 cm has length

2In a circle, chords AB and CD intersect at X inside the circle. AX = 4, XB = 6, CX = 3. Find XD.

3To construct an angle of 60° with a ruler and compasses, you construct

4ABCD is a cyclic quadrilateral with ∠ABC = 110° and ∠BAD = 75°. Find ∠ADC.

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

6The angle at the centre of a circle is 110°. The angle at the circumference on the same arc is

7Angles in the same segment of a circle are

8The angle between a tangent and a chord at the point of contact equals

9To construct an angle of 45°, you

10A chord of length 24 cm is in a circle of radius 13 cm. Its distance from the centre is