Follow Us on Twitter

Circle Theorem: The Angle in a Semicircle is 90° (Mathematics Lesson)

Circle Theorem: The Angle in a Semicircle is 90°

A triangle drawn from two ends of a diameter of a circle makes 90° at the circumference.

Why Is the Angle in a Semicircle 90°?

The circle theorem that the angle in a semicircle is 90° is a special case of the circle theorem that the angle at the center is twice the angle at the circumference.

The semicircle is bounded at the diameter. The angle made by the diameter at the center is 180°.



Let the angle at the circumference be θ.



The angle at the center is twice the angle at the circumference.



This is why the angle in a semicircle is 90°.

A Real Example of How to Use the Circle Theorem that the Angle in a Semicircle is 90°

The slider below shows a real example of the circle theorem that the angle in a semicircle is 90°:
Curriculum
Geometry Lessons
Interactive Test
  show
 
Note

WHAT IS A SEMICIRCLE

A semicircle is half a circle.

The curved edge is half a circumference, and the straight edge is the diameter.



ALL ANGLES IN A SEMICIRCLE ARE 90°

No matter on which point of the circumference the triangle is drawn to, the angle will be 90°.