In triangle ABC, it is known that AB = 7cm, C = 60 °. Find the diameter of the circle circumscribed about this triangle.

Find the diameter of the circumscribed triangle of the circle, if known:

Triangle ABC – rectangular;
AB = 7 cm;
Angle C = 60 °.
Decision:

The radius of the circumscribed circle of a right-angled triangle is half of the hypotenuse, since the center of the circle is equal to the center of the side of the hypotenuse.

We get:

R = 1/2 * AB = 1/2 * 7 cm = 7/2 cm = 3.5 cm;

Since the radius of the circle is equal to half the diameter of the circle, then we get the formula for the diameter:

d = 2 * R = 2 * 3.5 cm = 2 * 7/2 cm = 1 * 7/1 cm = 7/1 cm = 7 cm;

Answer: the diameter is 7 cm.