A chord,distance 2 cm from the centre,of a circle is 18 cm long.calculate the length of a chord of the same circle which is 6cm from the centre.
To solve this problem, we can use the formula for the relationship between the distances of two chords from the center of a circle. The formula is:
Length of chord 1 * Distance of chord 1 from the center = Length of chord 2 * Distance of chord 2 from the center
Let's plug in the given values:
Length of chord 1 = 18 cm
Distance of chord 1 from the center = 2 cm
Distance of chord 2 from the center = 6 cm
Length of chord 2 = ?
Using the formula, we have:
(18 cm) * (2 cm) = Length of chord 2 * (6 cm)
Simplifying the equation:
36 cm^2 = Length of chord 2 * 6 cm
To find the length of chord 2, divide both sides of the equation by 6 cm:
Length of chord 2 = 36 cm^2 / 6 cm
Simplifying further:
Length of chord 2 = 6 cm
Therefore, the length of the chord of the same circle that is 6 cm from the center is 6 cm.
r^2 = 2^2+9^2 = 85
so, if the unknown chord is 2x in length,
6^2+x^2 = r^2