Question

A chord 6 cm long is at distance of 4 cm from the centre of a circle. find the length of a chord which is at a distance of 3 cm from the centre of the circle

• A. 10 cm
• B. 6 cm
• C. 8 cm
• D. 12 cm

Answer 1

The correct option is C 8 cm

Give OC =4 cm, Chord AB =6 cm
$\because OC\perp AB\Rightarrow bisectsAB$
$\Rightarrow AC=CB=3cm$
$\therefore InOCA,O{A}^2+A{C}^2\left(PythagorasTheorem\right)$
$=4^2+3^2=16+9=25$
$\Rightarrow OA=5cm$
Let EF be the chord at a distance of 3cm from the centre.
GIven, radius=OE =5 cm
$\therefore In△OGE,E{G}^2=O{E}^2-O{G}^2=5^2-3^2=25-9=16$
$\Rightarrow EG=4cm$
$\therefore EF=2\times EG=8cm$
(Line from centre $\perp$ to chord bisects the chord )