Area of Triangle in Terms of Circumradius

Theorem
The area of $$\triangle ABC$$ is given by the formula $$(ABC)=\frac{a\cdot b\cdot c}{4r}$$ where $$r$$ is the circumradius and $$a$$, $$b$$ and $$c$$ are sides.

Proof


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Then by AA similarity $$\triangle AEC \sim \triangle DBC $$

$$ $$ $$

By area of a triangle, $$(ABC)=\frac{c\cdot h_c}{2}$$.

This gives us $$\frac{a\cdot b\cdot c}{4r}=(ABC)$$ as desired.