Question

the radius of a circle is 5 cm if the perpendicular drawn from the centre to a chord is 4cm then find the length of the chord​

Answer 1

Answer:

Radius of a circle, r = 5cm = AO=BO

Step-by-step explanation:

In triangle ACO,

By Pythagoras theorem:

(Hy)^2=(Per.)^2 + ( base)^2

(AO)^2=( OC)^2 + (AC)^2

(5)^2= (4)^2 + (AC)^2

25= 16 +(AC)^2

25- 16 = ( AC)^2

9 = ( AC)^2

Root 9 = AC

AC = 3 cm

We know that the perpendicular from the centre of the circle to a chord bisect the chord-

Then, AC= BC ( by theorem)

Hence, the length of the chord,

AB = AC + BC

= AC + AC

= 3 + 3

= 6cm

Hope it will help you.

Answer 2

Answer:

Radius of a circle is 5 cm.

Therefore OB = 5 cm.

Perpendicular drawn to the chord from the center bisects the chord.

Therefore AM = MB

Triangle OMB is right angled triangle at M

∠OMB=90 ∘

By Pythagoras theorem;

OB square  =OM square + MB square

MB=   OB  square - OM square

 MB=  5  square − 4  square

MB= 3 cm

So, the length of chord AB=2.

(MB)=6cm.

Step-by-step explanation:

hope it helps you