Question

Radius of a circle is 5 cm and distance of a chord from the centre is 3 cm. Hence the length of the chord is?​

Answer 1

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

∠OMA=90  ∘

 

by apply pythogoras theorm

OA  2  =OM  2  +MA  2

MA=  OA  2  −OM  2

MA=  5  2  −3  2

MA=  16

MA=4

therefore the length of chord AB=2MA

AB=8cm

option C will be the answer.

Answer 2

Answer:

It will be 8cm.

RADIUS: 5cm. LET RADIUS BE OA.

CHORD: 3cm away from the center (1 side of radius). LET CHORD BE OM.

The radius of a circle is 5cm, therefore OA= 5cm

The perpendicular drawn to the chord from the center bisects the chord.

Therefore AM=MB.

Triangle OMA is a right-angled triangle at M

∠OMA=90°

By applying Pythagoras theorem:

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

 $MA=\sqrt{OA^{2}-OM^{2}}$

$MA= \sqrt{5^{2} - 3^{2} }$  

$MA= \sqrt{16}$

​  

Therefore the length of chord AB=2MA

AB=8cm