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.

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.

- Circle definition
- Radius of a circle
- Diameter of a circle
- Circumference of a circle
- Parts of a circle (diagram)
- Semicircle definition
- Tangent
- Secant
- Chord
- Intersecting chords theorem
- Intersecting secant lengths theorem
- Intersecting secant angles theorem
- Area of a circle
- Concentric circles
- Annulus
- Area of an annulus
- Sector of a circle
- Area of a circle sector
- Segment of a circle
- Area of a circle segment (given central angle)
- Area of a circle segment (given segment height)

- Basic Equation of a Circle (Center at origin)
- General Equation of a Circle (Center anywhere)
- Parametric Equation of a Circle

- Arc
- Arc length
- Arc angle measure
- Adjacent arcs
- Major/minor arcs
- Intercepted Arc
- Sector of a circle
- Radius of an arc or segment, given height/width
- Sagitta - height of an arc or segment

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