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 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
General
Equations of a circle
Angles in a circle
Arcs
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