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Find the height and the radii of the inscribed and circumscribed circles of an equilateral triangle with side $a$.

#
In an isosceles triangle, the height drawn to the base is also the median, the angle bisector, and the perpendicular bisector of the base.

## Answer

$\frac{a \sqrt{3}}{2}, \frac{a \sqrt{3}}{6}, \frac{a \sqrt{3}}{3}$