Mathematics

Problem

Two equal chords

AB

and

CD

of length

14\,\text{cm}

are drawn on opposite sides of the centre

O

of a circle. The perpendicular distance between the two chords is

8\,\text{cm}

. a. (i) Show that each chord is

4\,\text{cm}

away from the centre. b. (ii) Calculate the radius of the circle. c. (iii) A third chord

EF

is drawn at a distance of

6\,\text{cm}

from the centre. Find the length of

EF

. d. Answer the following questions.