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semicircles

A semicircle is the half of a circle obtained by a diameter. It consists of the curved arc of the circle together with the straight line segment that connects the two endpoints of the arc.

The straight boundary is the diameter of the circle; the radius r is half the diameter d

The area of a semicircle equals half the area of a full circle: A = (1/2)πr^2. In terms

The curved boundary of a semicircle has length πr. The full boundary of a semicircle includes the

A semicircle is a circular sector with a central angle of 180 degrees. By Thales’ theorem, any

In coordinate terms, the upper semicircle of radius r centered at the origin is described by x^2

Applications include architecture and design, where semicircular arches and domes appear for structural and aesthetic reasons.

=
2r,
and
the
center
is
the
circle’s
center.
of
diameter
d,
this
becomes
A
=
(π/8)
d^2.
diameter,
giving
a
perimeter
P
=
πr
+
2r
=
r(π
+
2).
In
terms
of
diameter,
P
=
d(π
+
2)/2.
triangle
formed
on
a
semicircle
with
the
diameter
as
its
base
is
right-angled,
illustrating
the
special
role
of
semicircles
in
Euclidean
geometry.
+
y^2
=
r^2
with
y
≥
0.
They
also
serve
as
a
basic
geometric
shape
in
education,
often
used
to
illustrate
symmetry,
area,
and
arc-length
concepts.