7. AB is the diameter of a circle, centre O . C is a point on the circumference of the circle, such that |∠CAB| = 2 × |∠CBA| What is the size of ∠CBA ?
8. In the diagram on the right, |∠BAC| = 36° . O is the centre of the circle. Find the measure of the following angles, giving reasons for your answers.
(i) ∠ABC (ii) ∠ACB
9. In the diagram, | ∠BAC| = 38° . O is the centre of the circle. Find the measure of the following angles, giving reasons for your answers.
C
(i) ∠ABC (ii) ∠ACB
B
10. Find the value of x in each of the following diagrams (where O is the centre of each of the circles). (i)
(ii) 3x O 6x O 3x R
460 km O
430 km D IRELAND ENGLAND WALES SCOTLAND S
A O C B
O y
O C B A (iii) 24 cm O y 7 cm
12. Rockall (point R ) is a rocky outcrop off the coast of Donegal.
A O
Cathal would like to fi nd the distance between Donegal (point D) and the most westerly part of Scotland (point S). Using the diagram, fi nd the distance that Cathal wishes to fi nd. O is the centre of the circle in the diagram.
(iv) y O 17 m 15m y
37 cm O
11. Find the length of the side of the triangle marked with the letter y in each of the following diagrams (where O is the centre of each of the circles). (i)