#### Question

The lengths of two parallel chords of a circle are 6 cm and 8 cm. If the smaller chord is at distance 4 cm from the centre, what is the distance of the other chord from the centre?

#### Solution

Let AB and CD be two parallel chords in a circle centered at O. Join OB and OD.

Distance of smaller chord AB from the centre of the circle = 4 cm

OM = 4 cm

MB = AB/2 = 6/2 = 3cm

In ΔOMB,

OM^{2} + MB^{2} = OB^{2}

(4)^{2} + (3)^{2} = OB^{2}

16 + 9 = OB^{2}

OB^{2} = 25

`OB = sqrt25`

OB = 5cm

In ΔOND,

OD = OB = 5cm (Radii of the same circle)

ND = CD/2 = 8/2 = 4cm

ON^{2} + ND^{2} = OD^{2}

ON^{2} + (4)^{2} = (5)^{2}

ON^{2} = 25 - 16 = 9

ON = 3

Therefore, the distance of the bigger chord from the centre is 3 cm.

Is there an error in this question or solution?

Solution The lengths of two parallel chords of a circle are 6 cm and 8 cm. If the smaller chord is at distance 4 cm from the centre, what is the distance of the other chord from the centre? Concept: Cyclic Quadrilaterals.