English: Isosceles right triangle and
isosceles triangle with same circumscribed and inscribed circles, and same distance of their centers
![{\displaystyle d=r\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3b15f95735b7d56f4397c8af94c971371995e468)
. 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 }\!\,,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9af71d727a1c8ea66a9a7ef5ac6010828e4d9271)
![{\displaystyle \gamma =180^{\circ }-2\alpha \approx 34.062496^{\circ }\!\,.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fff854a130c4f92f0594f53ca23c9886503bb711)
Here radius of inscribed circle is:
![{\displaystyle r={\frac {a}{2}}\left(2-{\sqrt {2}}\right)\!\,,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/75b6bc1e56f58eee754051ecda1e9ca239b0ed34)
where a is length of equal sides of isosceles right triangle.
Made with GeoGebra 4.4.34.0 and Inkscape 0.48.3.1.
Slovenščina: Enakokraki pravokotni trikotnik in
enakokraki trikotnik z enakima očrtano in včrtano krožnico in enako razdaljo med njunima središčema
![{\displaystyle d=r\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3b15f95735b7d56f4397c8af94c971371995e468)
. Koti enakokrakega trikotnika so:
![{\displaystyle \alpha =\beta =\operatorname {arctg} {\frac {4-{\sqrt {2}}}{{\sqrt {2}}{\sqrt {8{\sqrt {2}}-11}}}}\approx 72,968751^{\circ }\!\,,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/311a4efe5f2fde31e1b2ea52e7d53fa9d4afdba4)
![{\displaystyle \gamma =180^{\circ }-2\alpha \approx 34,062496^{\circ }\!\,.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/072f6cf97f6bd88340121a6ab073aaab08895082)
Tu je polmer včrtane krožnice enak:
![{\displaystyle r={\frac {a}{2}}\left(2-{\sqrt {2}}\right)\!\,,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/75b6bc1e56f58eee754051ecda1e9ca239b0ed34)
kjer je a dolžina krakov enakokrakega pravokotnega trikotnika.
Izdelano z GeoGebra 4.4.34.0 in Inkscape 0.48.3.1.