Right triangle then with equality only in the isosceles case. If segments of lengths "p" and "q" emanating from vertex "C" trisect the hypotenuse into segments of length "c"/3, then The right triangle is the only triangle having two, rather than one or three, distinct inscribed squares. Let "h" and "k" ("h" > "k") be the sides of the two inscribed squares in a right triangle with hypotenuse "c". Then These sides and the incircle radius "r" are related by a similar formula: The perimeter of a right triangle equals the sum of the radii of the incircle and the three excircles:
Acute and obtuse triangles according to This implies that the longest side in an obtuse triangle is the one opposite the obtuse-angled vertex. An acute triangle has three inscribed squares, each with one side coinciding with part of a side of the triangle and with the square's other two vertices on the remaining two sides of the triangle. (In a right triangle two of these are merged into the same square, so there are only two distinct inscribed squares.) However, an obtuse triangle has only one inscribed square, one of whose sides coincides with part of the longest side of the triangle. All triangles