Question

The circles having radii r 1 and r2 intersect orthogonally Length of their common chord is

Answer 1

Let length of the common chord is `h`.
With the given details, we can create a diagram.
Please refer to video to see the figure.
Here, `/_BAC = 90^@, AB = r_1, AC = r_2`
`:. BC = sqrt(r_1^2+r_2^2)`
Now, Area of `Delta ABC = 1/2**AB**AC = 1/2**(r_1r_2)`
Also, Area of `Delta ABC = 1/2**BC**h/2 = h/2sqrt(r_1^2+r_2^2)`
`:.1/2**(r_1r_2) = h/4sqrt(r_1^2+r_2^2)`
`=>h = (2r_1r_2)/(sqrt(r_1^2+r_2^2)`,which is the length of common chord.