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

Geometry
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

- 5.5 cm
- 5 cm
- 3.5 cm
- 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.

OP^{2} + PB^{2} = OB^{2}

OQ^{2} + QD^{2} = OD^{2}

Subtracting second equation from the first

OP^{2} - OQ^{2} + PB^{2} - QD^{2} = OB^{2} - OD^{2}

(OP - OQ)(OP + OQ) = 6^{2} - 2.5^{2} = (6 - 2.5)(6 + 2.5)

OE - OF = 3.5 cm

**The correct option is C.**