In triangle ABC, the angle at the vertex C is 90 degrees and the outer angle at the vertex A is 150 degrees. The smaller side of the triangle is 12.5. Find the length of the diameter of the circle described around this triangle.
The angle BAC is adjacent to the outer corners BAD, then the angle BAC = 180 – BAD = 180 – 150 = 30.
The BC leg lies against an angle of 30, then AB = 2 * BC = 2 * 12.5 = 25 cm.
Since triangle ABC is rectangular, the diameter of the circumscribed circle around it coincides with the hypotenuse of the triangle.
Then D = AB = 25 cm.
Answer: The diameter of the circumscribed circle is 25 cm.
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