Question

4. In a circle of radius 5 cm, AB and CD are two parallel chords of lengths
8 cm and 6 cm respectively. Calculate the distance between the chords
if they are
(i) on the same side of the centre,
(ii) on the opposite sides of the centre,​

Answer 1

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OA = OC = 5cm, AB = 8cm and CD = 6cm

=> AL = 4cm and CM = 3cm (Perpendicular from the centre bisects the chord).

In right triangles OLA and OMC, by Pythagoras Theorem —

OA² = OL² + AL² and OC² = OM² + CM²

=> 5² = OL² + 4² and 5² = OM² + 3²

=> OL² = 9 and OM² = 16

=> OL = 3 and OM = 4

(i) In first case distance between AB and CD is

LM = OM - OL

= 4 - 3 = 1cm

(ii) In second case distance between AB and CD is

LM = OM + OL

= 4 + 3 = 7cm

Answer => (i) 1cm and (ii) 7cm.

Step-by-step explanation:

$\huge \fbox \red {Hope \: it \: helps \: you}$