Question

The lengths of parallel chords which are on opposite sides of the centre of a circle are 6 cm and 8 cm. If radius of the circle is 5 cm, then the distance between these chords is ______.

Options

• 2 cm

• 1 cm 

• 8 cm

• 7 cm

Answer 1

The lengths of parallel chords which are on opposite sides of the centre of a circle are 6 cm and 8 cm. If radius of the circle is 5 cm, then the distance between these chords is 7 cm.

Explanation:

Let the chords be AB = 6 cm and CD = 8 cm

O be the centre with OA = OC = 5 cm as radius.

OE ⊥  AB and OF ⊥  CD
In ΔAEO,

AE² + EO² = AO²

⇒ 3² + EO² = 5²

⇒ 9 + EO² = 25

⇒ EO² = 16

⇒ EO = 4 cm

In ΔOFC,

OF² + CF² = OC²

⇒ OF² + 4² = 5²

⇒ OF² + 16 = 25

⇒ OF² = 9

⇒ OF = 3 cm

EF = EO + OF

= 4 + 3 cm

= 7 cm

∴ The distance between the two chords is 7 cm.