Find the length of the chord which is at 12 cm distance from center and radius of circle is 13cm.

Explanation

Given that
The distance of chord from centre = `12 cm`
Radius = `13cm`
The length of the chord will be `10 cm`.
We can easily solve this problem by following the given steps.
Now,
Let's take the centre of the circle to be `A`, the chord to be `BC` and the point on the chord from the centre to be `D`.
So,
`AB = AC = 13 cm `(radius of the circle)
`AD = 12 cm` (distance of the chord from the centre)
The two right-angled triangles will be formed.` ( triangle ADB and triangle ADC)`
Using Pythagoras theorem in `triangleADB,`
`AB^2 = AD^2 + BD^2`
`BD^2= AB^2 - AD^2`
`BD^2 = (13)^2 - (12)^2`
`BD^2= 169 -144`
`BD^2 = 25`
`BD = sqrt25`
`BD = 5 cm`
The chord is `BC` that is the sum of `BD` and `DC`.
`DC` will be equal to `BD` as the `AC` is equal to `AB` and `AD` is common.
`BD = DC = 5 cm`
Length of the chord, `BC = BD + DC`
Length of the chord = `(5+5) cm`
Hence, the length of the chord will be `10 cm`.