Graduate Management Admission Test (GMAT) Practice Test

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

Equilateral triangle

Scalene triangle

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.

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Isosceles triangle

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