Question

if O is the centre of the circle with radius 5cm . chords AB and CD are parallel and are on the same side of centre ,AB =6cm,CD= 8cm. if PQ is distance between ab and cd then find PQ

Answer 1

Let AB and CD be two chords of a circle such that AB || CD which are on the same side of the circle. Also AB = 8 cm and CD = 6 cm, OB = OD = 5 cm. Join OL and LM.

Since the perpendicular from the centre of a circle to a chord bisects the chord.


We have LB=12×AB

= =(12×8) cm = 4 cm

And MD=12×CD

= =(12×6) cm = 3 cm

Now, in rt  angled Δ BLO, we have

OB² = LB² + LO²

⇒ LO² = OB² – LB²

= 5² – 4²

= 25 – 16 = 9

∴ LO=9–√ = 3 cm

Again in rt  angled Δ DMO, we have

OD²  = MD²  + MO²

MO²  = OD²  – MD²

= 5²  – 3²

= 25 – 9 =16

⇒ MO=16−−√ = 4 cm

∴ The distance between the chords = (4 – 3) cm = 1 cm