Shape and Space 2
4 marks · NormalThe diagram shows a circle with centre O. The radius of the circle is 5 cm. Chord AB is 8 cm long.
Find the perpendicular distance from O to AB.
Explain why this line bisects AB.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) 3 cm
(b) The perpendicular from the centre to a chord bisects the chord.
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Draws appropriate right-angled triangle, or writes (lets distance = x and AM = 4 cm).
A1 (a) · 2 marks · Uses Pythagoras’ theorem to find x = 3 cm (accept correct working with answer in range)
B1 (b) · 1 mark · Gives correct reason: 'The perpendicular from the centre to a chord bisects the chord.'
Worked solution
Let M be the midpoint of AB, so AM = 4 cm. Triangle OMA is right-angled with hypotenuse OA = 5 cm and AM = 4 cm.
The perpendicular from the centre to a chord bisects the chord, so M is the midpoint.