# In triangle ABC, the angle at the vertex C is 90 degrees and the outer angle at the vertex A is 150 degrees.

October 8, 2021 | education

| **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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