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In an acute triangle, the sum of the circumradius R and the inradius r is less than half the sum of the shortest sides a and b: [4]: p.105, #2690 + < +, while the reverse inequality holds for an obtuse triangle. For an acute triangle with medians m a, m b, and m c and circumradius R, we have [4]: p.26, #954
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In geometry, an isosceles triangle (/ aɪ ˈ s ɒ s ə l iː z /) is a triangle that has two sides of equal length or two angles of equal measure. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case.
A triangle in which one of the angles is a right angle is a right triangle, a triangle in which all of its angles are less than that angle is an acute triangle, and a triangle in which one of it angles is greater than that angle is an obtuse triangle. [8] These definitions date back at least to Euclid. [9]
Diagram to show that the circumcentre of an acute triangle is inside the triangle. One in a series. Date: 13 April 2007: Source: Own drawing, Inkscape 0.45: Author: Inductiveload: Permission (Reusing this file)
English: Euler diagram of types of triangles, using the definition that isosceles triangles are triangles with at least 2 equal sides (that is, equilateral triangles are isosceles triangles). Date 17 April 2011