A circle is inscribed in a right quadrangle with a side of 4 cm. Find a) the radius of the circle

A circle is inscribed in a right quadrangle with a side of 4 cm. Find a) the radius of the circle b) the side of a regular triangle circumscribed about a given circle.

A regular quadrilateral is a square.
Let the sides of the square be equal to a, a = 4.
A) The radius of the inscribed circle is perpendicular to one of the sides of the square at the point of contact, and is equal to half of the side of the square, that is
R = a / 2 = 4/2 = 2 (cm).
B) Now we find the radius of a circle circumscribed around an equilateral triangle using the formula from the general formula:
R = a * b * c / (4 * S), where a, b, c are the sides of an arbitrary triangle, S is the area of ​​the triangle.
A special case when the triangle is equilateral and, using the theorem of sines:
R = b / (2 * sin α), in an equilateral triangle all angles are 60, b is the side of an equilateral (regular) triangle.
R = b / (2 * sin 60), sin 60 = √3 / 2.
R = b / √3.
b = R * √3 = 2√3 (cm).