The length of a circle circumscribed about a right-angled triangle is 26pi cm

The length of a circle circumscribed about a right-angled triangle is 26pi cm, and the length of one of the legs is 10 cm. Calculate the area of the triangle.

Using the formula for the circumference of a circle, we determine the diameter of the circle, which will be equal to the length of the hypotenuse of a right-angled triangle.

As a result of the calculation, we get 26 Pi / Pi = 26 cm.

Then, applying the Pythagorean theorem, we calculate the second leg of the right triangle.

When we count, we will have a leg equal to √ (26 x 26 – 10 x 10) = √ (676 – 100) = √576 = 24 cm.

Now let’s determine the area of a right-angled triangle.

We get 24 x 10/2 = 240/10 = 120 cm ^ 2.

Answer: 120 cm ^ 2.