Graduate Management Admission Test (GMAT) Practice Test

If a triangle is inscribed in a circle such that one of its sides is a diameter, what type of triangle is formed?

1. Equilateral triangle

2. Scalene triangle

3. Right triangle

4. Isosceles triangle

The correct answer is: Right triangle

When a triangle is inscribed in a circle with one of its sides as the diameter, we can apply a theorem from geometry known as the Inscribed Angle Theorem, which states that an angle inscribed in a semicircle is a right angle. This means that if a triangle has one side that is the diameter of the circle, then the opposite vertex will subtend an angle of 90 degrees. Therefore, the triangle formed is specifically a right triangle, since one of its angles is exactly 90 degrees. The other two angles will be acute, but the defining characteristic here is that the triangle must contain a right angle due to the position of the diameter. Understanding this property helps us recognize that any triangle that adheres to this configuration guarantees that it will always be a right triangle, regardless of the lengths of the other two sides.