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
Answers
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:
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