Find the radius of a circle circumscribed about a triangle whose vertices have coordinates (-4; -2) (-4; 4) (4; 4).

It is known from the condition that the triangle is given by the coordinates of its vertices A (-4; -2); B (-4; 4) and C (4; 4).

We need to find the radius of the circle circumscribed around this triangle.

If we construct a triangle on the plane along the coordinates, we will see that it is rectangular, with a hypotenuse AC.

We calculate the length of the hypotenuse of the triangle, apply the formula:

AC = √ (xc – xa) ^ 2 + (yc – ya) ^ 2 = √ (4 + 4) ^ 2 + (4 + 2) ^ 2 = √ (16 + 36) = √52 = 2√13;

The radius of a circle circumscribed about a right-angled triangle is half the hypotenuse:

R = 2√13 / 2 = √13.