Semi in Latin means half. Semicircle by itself means half circle.
In Geometry, semicircle can be defined as a 2-dimensional figure that forms half of a circle is called Semicircle. It is a closed shape that is half a circle but diameter of that circle. Which means the diameter of a circle cuts the circle into two equal semicircles.
A circle makes a full turn of 360°. Semicircle being half a circle measures half of circle’s 360°, thus measuring 180°.
An angle inscribed in a semicircle is always 90 °.
Proof: We have to prove that ∠ACB = 90 °
Mark Centre O. Join OC.
Now, OA = OB =OC = radius.
Δ OCA and Δ OCB are isosceles triangles.
Since the base angles of an isosceles triangle are equal,
We have ∠ OCB = ∠ OBC and ∠ OCA = ∠ OAC.
Also, Sum of angles in a triangle = 180 °
Thus, ∠ OAC + ∠ ACB +∠ OBC = 180°.
∠ OAC + ∠ OCA + ∠ OCB +∠ OBC = 180° (Since ∠ ACB = ∠ OCA + ∠ OCB)
2∠ OCA + 2∠ OCB = 180°.
2(∠ OCA + ∠ OCB) = 180°.
∠ OCA + ∠ OCB = 90°.
∠ ACB =90° (Since ∠ ACB = ∠ OCA + ∠ OCB)
Any triangle inscribed in semicircle is always a right triangle.