What is the significance of angles subtended by a diameter in a circle?

The angle subtended by a diameter at any point on the circumference of a circle is always 90 degrees. This is a fundamental property of circles that stems from the inscribed angle theorem, which states that an angle inscribed in a semicircle is a right angle.

When you draw a diameter of a circle and then connect the endpoints of that diameter to another point on the circle, the angle formed at that circumference by the two radii will always measure 90°. This characteristic is critical in various geometric proofs and constructions.

Understanding this concept is important because it helps in solving problems involving circles, particularly in determining relationships between different angles or segments within circular geometry.