The vertices of a triangle with sides 2, 4√2, 6 cm lie on a sphere. Find the radius of the sphere if the plane

The vertices of a triangle with sides 2, 4√2, 6 cm lie on a sphere. Find the radius of the sphere if the plane of the triangle is 4 cm from its center.

Let’s define the type of triangle ABC.
AC = 6 cm its largest side AC ^ 2 = 36.
AB ^ 2 + BC ^ 2 = 32 + 4 = 36.
Then the triangle ABC is rectangular, and therefore the point O1 is the middle of the hypotenuse AC.
AO1 = AC / 2 = 6/2 = 3 cm.
The segment OO1 is perpendicular to the AC, then the triangle OO1A is rectangular, and its hypotenuse OA is the radius of the sphere.
By the Pythagorean theorem, OA ^ 2 = AO1 ^ 2 + OO1 ^ 2 = 9 + 16 = 25.
ОА = R = 5 cm.
Answer: The radius of the sphere is 5 cm.