In the triangle ABC, it is known that AC = 3, BC = √55, the angle C is 90 °. Find the radius of the circumscribed

In the triangle ABC, it is known that AC = 3, BC = √55, the angle C is 90 °. Find the radius of the circumscribed circle of this triangle.

Given ∆АВС with angle C = 90 °. The ABC triangle is rectangular and its legs are equal:

| AS | = 3;

| Sun | = √55;

The center of a circle circumscribed around a right-angled triangle coincides with the point dividing the hypotenuse in half. The radius R of this circle is half the length of the hypotenuse.

Let’s write down the Pythagorean theorem:

| AC | ^ 2 + | BC | ^ 2 = | AB | ^ 2;

and find the hypotenuse AB:

| AB | ^ 2 = 3 ^ 2 + (√55) ^ 2 = 9 + 55 = 64;

| AB | = √64 = 8;

For the radius R we get:

R = | AB | / 2 = 8/2 = 4:

Answer: the radius of the circumscribed circle is 4