Question

Determine the length of a chord which is at a distance of 6 cm from the centre of a circle of radius 10 cm.

• A. 12 cm
• B. 14 cm
• C. 16 cm
• D. 18 cm

Answer 1

The correct option is C

16 cm

Let AB be a chord of a circle with centre O and radius 10 cm.

Draw OC and AB. Join OB

In $△$BCO, We have

OC = 6 cm

and

OB = 10 cm

BC = $\sqrt{{OB}^2-{OC}^2}$

BC = $\sqrt{{10}^2-6^2}$

BC = $\sqrt{100-36}$

= $\sqrt{64}$
BC = 8 cm
AB = AC + BC
AB = BC + BC [Since the perpendicular from the centre to a chord bisects the chord AC = BC]
AB = 2BC
Hence,

AB = 2 × 8 = 16 cm