Angle inscribed in a semicircle

The angle inscribed in a semicircle is always a right angle (90°).
Try this Drag any orange dot. The inscribed angle ABC will always remain 90°.

The line segment AC is the diameter of the semicircle. The inscribed angle is formed by drawing a line from each end of the diameter to any point on the semicircle. No matter where you do this, the angle formed is always 90°. Drag the point B and convince yourself this is so. This is true regardless of the size of the semicircle. Drag points A and C to see that this is true.

The triangle formed by the diameter and the inscribed angle (triangle ABC above) is always a right triangle.

Relationship to Thales' Theorem

This is a particular case of Thales Theorem, which applies to an entire circle, not just a semicircle.

Thales theorem Thales Theorem states that any diameter of a circle subtends a right angle to any point on the circle. (see figure on right).

No matter where the point is, the triangle formed is always a right triangle. See Thales Theorem for an interactive animation of this concept.

Other circle topics


Equations of a circle

Angles in a circle