Question 96
Let $O$ be the circumcenter of the acute triangle $ABC$ and let $M$ be an arbitrary point on the side $AB$. The circumference circumscribed to the triangle $AMO$ intersects for the second time to the line $AC$ at the point $K$ and the circumference circumscribed to the triangle $BOM$ intersects the line $BC$ for the second time at the $N$ point. Test that $$
\text{Area}(MNK) \geq \frac{1}{4} \text{Area}(ABC)
$$ and determine the case where equality is achieved.
\text{Area}(MNK) \geq \frac{1}{4} \text{Area}(ABC)
$$ and determine the case where equality is achieved.