Angle in a semicircle

Objective

To verify that angle in a semi-circle is a right angle, using vector method.

Semicircle

A semi-circle is half a circle. The curved edge is half a circumference, and the straight edge is the diameter.

What are angles in a semicircle?

  • Angles in a semi-circle are created when you join the two ends of the diameter to one point on the arc using chords.
  • In the diagram above, AC is the diameter of a circle that divides the circle into two.
  • The two points A and C are joined to another point B on the circumference using two chords.
  • This triangle is a right-angle triangle with the 90° angle touching the arc. This is the same for any point that is placed on thye arc.
  • If the point is placed on another point in a semicircle, the result would be the same(the two chords would meet at the circumference at 90°).
  • The angle in a semicircle is 90°