Two equal chords and of length are drawn on opposite sides of the centre of a circle

MATHEMATICS · Multi-part · CBSE · Mathematics · Circles · Circles

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.