Radius of a circle with Centre p is 20 CM and the distance of its chord from the centre is 12cm find the length of the chord
Answers
Given:
The radius of a circle with Centre p is 20 CM and the distance of its chord from the centre is 12cm
To Find:
find the length of the chord
Solution:
A chord is a line segment from one point of the circle to the other. It is given that the distance of the chord from the centre of a circle is 12cm which means that the perpendicular drawn from the centre to the chord has a length of 12 cm.
So we can see a triangle forming by joining the two ends of the chord with the centre and each triangle formed is a right-angled triangle
Now to find the length of the chord we will use the Pythagoras theorem in one of the triangles formed,
In triangle OPB, where
OP=12cm
OB=20cm
[tex]OB^2=OP^2+PB^2\\ 20^2=12^2+PB^2\\ PB=\sqrt{400-144}\\ PB=16cm[/tex]
So now the length of the chord will be two times PB
Chord=16*2
=32cm
Hence, the length of the chord is 32cm.
Given:
The radius of the circle is 20cm
The center of the circle is P
The distance between the chord and from the center = 12cm
To Find:
the length of the chord.
Solution:
The distance from the chord to the center i.e.
PC ⊥ AB
Let the triangle in the circle be ACP,
In ΔACP,
Using Pythagoras theorem
⇒ AP² = PC² + AC²
⇒ AC² = AP² - PC²
⇒ AC² = (20)² - (12)²
⇒ AC² = 400 - 144
⇒ AC² = 256
⇒ AC = √256
⇒ AC = 16
Now,
AB = AC + CB [center bisects the chord]
AC = CB
AB = 2AC
= 2 × 16
= 32cm
AB is the chord of the circle.
Therefore, the length of the chord = 32cm