Question

Find the length of a chord which is at a distance of $3$ cm from the centre of a circle of radius $5$ cm.

• A. $2$ cm
• B. $6$ cm
• C. $8$ cm
• D. $10$ cm

Answer 1

Answer: (C)

$8$ cm

Radius of a circle is 5cm

therefore OA= 5cm

perpendicular drawn to the chord from the centre bisects the chord

therefore AM=MB

triangle OMA is right angled triangle at M

$\angle OMA={90}^{\circ }$

by apply pythogoras theorm

${OA}^2={OM}^2+{MA}^2$

$MA=\sqrt{{OA}^2-{OM}^2}$

$MA=\sqrt{5^2-3^2}$

$MA=\sqrt{16}$

$MA=4$

therefore the length of chord AB=2MA

AB=8cm

option C will be the answer.