A circle is circumscribed about a right-angled triangle ABC. Find the angle C if AB = AC.

In this task, we find the value of the angle C;

To do this, we introduce the designation of the angles by the corresponding letters A, B, C;

Since the triangle is rectangular (one of the angles is 90 °), and the two sides of this triangle are equal, it means that it is also isosceles;

And from the properties of an isosceles triangle, we know that the angles at the base are equal, which means A = C, B = 90 °;

Since the sum of all the angles of any triangle is 180 °, then you can write the equation;

180 ° = A + B + C;

Since A = C, then;

180 ° = 2A + 90;

2A = 90;

A = 90/2;

A = C = 45 °.