A circle is circumscribed about an isosceles triangle ABC with a base angle of 30 degrees and

A circle is circumscribed about an isosceles triangle ABC with a base angle of 30 degrees and a lateral side of 10. Find the radius of this circle.

1. From the vertex B of the triangle ABC, let us lower the height BH to the base of the AC. In the AВН triangle, the AВН angle is 90 – 30 = 60 degrees.

2. Connect the center of the circle O with the vertices A and B of the triangle ABC. The segment OA and OB are the radii of the circle.

3. Consider a triangle ABO. The OВA angle is equal to the OВA angle and is equal to 60 degrees. The angle AOB is

180 – (60 + 60) = 60 degrees. The ABO triangle is equilateral, that is, AO is equal to OB, equal to AB, equal to 10 centimeters.

Answer: The radius of the circle is ten centimeters.