Question

(2) In a circle of radius 5 centimetres, two parallel chords of lengths
6 and 8 centimetres are drawn on either side of a diameter. What is the
distance between them? If parallel chords of these lengths are drawn
on the same side of a diameter, what would be the distance between
them?​

Answer 1

Answer:

here in the above fig o is the radius MN and PQ are the chords where

MN = 6 cm

PQ= 8 cm

radius ON=OQ=5 cm.

in a traingle OAN

AN =6/2 =3 cm [the perpendicular drawn from the center to the chord bisects the chords.]

now using pythogorean theorem

ON^2= OA^2 +AN^2

5*5= OA^2 +3*3

OA= 4 cm.

similarly in traingle OBQ

OQ=4 cm.

from the similar process above

OB= 3 cm

NOW the distance between them is AB= AO+OB = 4+3 = 7cm.