A chord of length 12 CM is at a distance of 12 CM from the centre of a circle. Determine the length of the chord of the same circle is of length 24 CM. Find its distance from the centre
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We know that we can get the distance between the chord and center if the line from center is perpendicular to the chord . So the chord will be divided into two equal parts of 6 cm each ( because a line perpendicular to the chord divides it into two equal parts ) . The distance between the center and the chord is 12 cm
So by Pythagoras Theorum we can find the radius of the circle which will be done as follows,
Let r be the radius
Therefore, r^2 = 12^2 +6^2
=144+36
r=√180
Now on the other side the length of the another chord is 24 so if the line perpendicular to the chord will divide it into two parts of 12cm each
so by Pythagoras Theorum,
r^2=12^2+l^2 (where l is the distance from the center to the chord)
(√180)^2=144+l^2
180-144=l^2
l=√36
l=6
Therefore the distance between the second chord and the center is 6.
So by Pythagoras Theorum we can find the radius of the circle which will be done as follows,
Let r be the radius
Therefore, r^2 = 12^2 +6^2
=144+36
r=√180
Now on the other side the length of the another chord is 24 so if the line perpendicular to the chord will divide it into two parts of 12cm each
so by Pythagoras Theorum,
r^2=12^2+l^2 (where l is the distance from the center to the chord)
(√180)^2=144+l^2
180-144=l^2
l=√36
l=6
Therefore the distance between the second chord and the center is 6.
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