A chord distance 2cm from the centre of a circle is 18 cm long. calculate the length of a chord of the same circle which is 6 cm distance from the centre?
Answers
Given,
The length of the first chord = 18 centimetres
The distance between the centre of the circle and the first chord = 2 centimetres
The distance between the centre of the circle and the second chord = 6 centimetres
To find,
The length of the second chord.
Solution,
If we compare the half of the first chord with the base of right angle triangle, the perpendicular distance from the the centre with the perpendicular of a right angle triangle and the radius of the circle with the hypotenuse of a right angle triangle,then we will get a perfect right angle triangle.
So,we can find out the length of the radius of the circle by using the Pythagoras theorem.
Half of chord = 18/2 = 9 cm = Base
Perpendicular distance = 2 cm = Perpendicular
Radius = Let, x cm = Hypotenuse [Assume, x as a variable to do the further mathematical calculations.]
Now, according to the Pythagoras theorem,
x² = (9)²+(2)²
x² = 81 + 4
x² = 85
x = ✓85
Radius of the circle = ✓85 cm
Now,for the second chord,
Half of chord = Let, y cm = Base [ Assume, y as a variable to do the further mathematical calculations.]
Perpendicular distance = 6 cm = Perpendicular
Radius of the circle = ✓85 cm = Hypotenuse
According,to the Pythagoras theorem,
(✓85)² = (y)² + (6)²
85 = y² + 36
y²+36 = 85
y² = 85-36
y² = 49
y = 7
Half length of the chord = 7 cm
Full length of the chord = 7×2 = 14 cm
Hence,the length of the chord will be 14 centimetres.