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

Explanation

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)`

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