The triangle has two 45 ° angles. Find the perimeter of this triangle if the radius of the circle around it is √8.

In a triangle, by condition, two angles are equal to 45, then its third angle is (180 – 45 – 45) = 90, which means that the triangle is rectangular and isosceles, AC = BC.

If a right-angled triangle is inscribed in a circle, then its hypotenuse lies on the diameter of the circle. AB = 2 * R = 2 * √8 = 4 * √2 cm.

Then AC ^ 2 + BC ^ 2 = AB ^ 2.

2 * AC ^ 2 = 32.

AC ^ 2 = 32/2 = 16.

AC = BC = 4 cm.

Then Ravs = AC + BC + AB = 4 + 4 + 4 * √2 = 4 * (2 + √2) cm.

Answer: The perimeter of the triangle is 4 * (2 + √2) cm.