# Semicircle

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°.

### Thales' theorem

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)

Hence proved.

*Any triangle inscribed in semicircle is always a right triangle.*