Question

What is the distance between two parallel chords of length 24 cm and 32 cm in a cirle of radius 20 cm, given they are on same side?

Answer 1

There are 2 possibilities :

Both chords on opposite side of the centre.

Both side on the same side from the centre.

Opposite side:

Perpendicular from the centre to the chord, bisects the chord.

Hence PB = 12 and QA = 16.

Now apply Pythagoras theorem.

OP2 = OB2 - PB2 = 400 – 144 = 256. OP = 16.

OQ2 = OA2 - QA2 = 400 – 256 = 144. OQ = 12.

Hence, the distance is sum of OP and OQ is 28.

Same side :

We get OP as 16 and OQ as 12 (explained above).

Since they are on the same side, the distance between them is 4. (16 – 12)