Two parallel chords of a circle whose diameter is 13 cm are respectively 5 cm and 12 cm

Two parallel chords of a circle whose diameter is 13 cm are respectively 5 cm and 12 cm in length. If both the chords are on the same side of the diameter, then the distance between these chords is

  1. 5.5 cm
  2. 5 cm
  3. 3.5 cm
  4. 3 cm

Answer

Draw a perpendicular from the centre (O) of the circle to the chords AB and CD. The perpendicular bisects the chords at P and Q respectively.

OP2 + PB2 = OB2

OQ2 + QD2 = OD2

Subtracting second equation from the first

OP2 - OQ2 + PB2 - QD2 = OB2 - OD2

(OP - OQ)(OP + OQ) = 62 - 2.52 = (6 - 2.5)(6 + 2.5)

OE - OF = 3.5 cm

The correct option is C.