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Circle Theorem: Angle in a Semicircle Is 90°
(KS3, Year 8)

homegeometryangle in a semicircle is 90°
A triangle drawn from two ends of a diameter of a circle makes an angle of 90° at the circumference. It is a right triangle because the angle at the circumference is a right angle.

circle theorem angle in semicircle is 90 degrees

Why Is the Angle in a Semicircle 90°?

The circle theorem where the angle in a semicircle is 90° is a special case of the circle theorem where 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°. angle_at_diameter Let the angle at the circumference be θ. angle_at_circumference_semicircle The angle at the center is twice the angle at the circumference.

180° = 2 × θ

θ = 180° ÷ 2

θ = 90°

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

Lesson Slides

The slider below shows a real example of the circle theorem that the angle in a semicircle is 90°.

What Is a Semicircle?

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

semicircle mini

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°.

all angles in semicircle
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This page was written by Stephen Clarke.

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