Question

In a circle, a chord 3 centimetres away from the centre is 8 centimetres long. How long is a chord, 1.4 centimetres away from the centre in this circle?

Answer 1

Let AB and CD are the two chords in which AB = 8 cm, OF = 3 cm and OE = 1.4 cm.

Construction: Join OA and OC.

We know that AB = 2AF = 2, where r is the radius of the circle and d₁ is the perpendicular distance of AB from the centre of the circle.

⇒ 8 = 2

⇒ = 4

⇒ r² − 3² = 4²

⇒ r² = 16 + 9 = 25

⇒ r = 5

Therefore, the radius of the circle is 5 cm.

Similarly, CD = 2CE = 2, where r is the radius of the circle and d₂ is the perpendicular distance of CD from the centre of the circle.

⇒ CD = 2

⇒ 2 = CD

⇒ CD = 2 ×

⇒ CD = 2 × 4.8 = 9.6

Thus, a chord of length 9.6 cm is at a distance of 1.4 cm from the centre of the circle.