English: Isosceles right triangle and isosceles triangle with same circumscribed and inscribed circles, and same distance of their centers ${\displaystyle d=r\,}$. Angles of isosceles triangle are:

${\displaystyle \alpha =\beta =\arctan \left({\frac {4-{\sqrt {2}}}{{\sqrt {2}}{\sqrt {8{\sqrt {2}}-11}}}}\right)\approx 72.968751^{\circ }\!\,,}$

${\displaystyle \gamma =180^{\circ }-2\alpha \approx 34.062496^{\circ }\!\,.}$

Here radius of inscribed circle is:

${\displaystyle r={\frac {a}{2}}\left(2-{\sqrt {2}}\right)\!\,,}$

where a is length of equal sides of isosceles right triangle.

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