# What does this figure signify?

I made this after I saw a similar problem in our module, where we were given above defined $$\omega$$ and I developed on the circumcircles using properties of circles.

$$\cot(A) + \cot(B) + \cot(C) = \cot(\omega)$$

and

$$\csc^2(\omega) = \csc^2(A) + \csc^2(B) + \csc^2(C)$$

Can we take any help from this circles help in proving the above identities?

I joined each center with $$O$$ to obtain an isosceles triangle and something like -

$$(\cot(\omega) - \cot(A))(\cot(\omega) - \cot(B))(\cot(\omega) - \cot(C)) = \frac{1}{\sin(A)\sin(B)\sin(C)}$$

I am missing something.

Note by Kartik Sharma
1 year, 5 months ago

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