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# Area of a special triangle

In $$\Delta ABC$$ if $$A,B,C$$ are the measures of angles , $$I,O,H$$ are incenter, circumcenter, orthocenter respectively, prove that:

$\large [IOH]=\left| 2R^2\sin\left(\dfrac{B-C}{2}\right)\sin\left(\dfrac{C-A}{2}\right)\sin\left(\dfrac{A-B}{2}\right)\right|$

• $$[IOH]$$ indicates area of $$\Delta IOH$$.

Note by Nihar Mahajan
1 year, 12 months ago