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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' TheoremThis 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 topicsGeneral
Equations of a circle
Angles in a circleArcs
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