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°.
Let the angle at the circumference be θ.
The angle at the center is twice the angle at the circumference.
180° = 2 × θ
θ = 180° ÷ 2
θ = 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.
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°.
This page was written by Stephen Clarke.
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