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Isosceles triangle
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===Radii=== [[File:Isosceles-triangle-more.svg|thumb|Isosceles triangle showing its circumcenter (blue), centroid (red), incenter (green), and symmetry axis (purple)]] The inradius and circumradius formulas for an isosceles triangle may be derived from their formulas for arbitrary triangles.{{sfnp|Harris|Stöcker|1998|page=75}} The radius of the [[inscribed circle]] of an isosceles triangle with side length <math>a</math>, base <math>b</math>, and height <math>h</math> is:{{sfnp|Harris|Stöcker|1998|page=78}} :<math>\frac{2ab-b^2}{4h}.</math> The center of the circle lies on the symmetry axis of the triangle, this distance above the base. An isosceles triangle has the largest possible inscribed circle among the triangles with the same base and apex angle, as well as also having the largest area and perimeter among the same class of triangles.{{sfnp|Alsina|Nelsen|2009|page=67}} The radius of the [[circumscribed circle]] is:{{sfnp|Harris|Stöcker|1998|page=78}} :<math>\frac{a^2}{2h}.</math> The center of the circle lies on the symmetry axis of the triangle, this distance below the apex.
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