Two parallel chords 10 centimeters and 24 centimeters long are drawn on the same side of the centre of a circle of radius 13 centimeters. Find the distance between the chords.
7 cm
We need to find PQ in the above figure.
Since perpendicular from the centre to a chord bisects the chord, we must have AP = BP = 12 cm and CQ = DQ = 5 cm.
We know, in a circle, the square of half the length of a chord is the difference of the squares of the radius and the perpendicular distance of the chord from the centre of the circle.
So, AP2=OA2−OP2
⟹OP2=OA2−AP2
⟹OP2=132−122=169−144=25=52
⟹OP=5 cm
Similarly,
OQ=√OC2−CQ2=√132−52=12 cm
Now, PQ=OQ−OP=12cm−5cm=7cm
Therefore the distance between the chords is 7 cm.