THE CIRCLE
THEROM
GROUP MEMBERS
Alicia Phillips
Ann-Marie Thompson
Kishawnie Sewell
Deshaun Walker
Davihano Pottinger
10s
THE
CIRCLE
T
H
E
O
R
E
M
o A circle is a round plane
figure whose boundary (the
circumference) consists of
points equidistant from a
fixed point (the centre)
o The Circle Theorem is the
angle that lies between a
tangent and a cord is equal
to the angle subtended by
the same chord in the
alternate segment.
When two angles are
subtended by the same
arc, the angle at the
centre of a circle is
twice the angle at the
circumference. So
angle AOB = 2 × angle
ACB. Angles
subtended by the same
arc at the
circumference are
equal. This means that
angles in the same
segment are equal
.
THE PROPERTIES OF THE
CIRCLE
Lines and circles are the important elementary figures in
geometry. We know that a line is a locus of a point
moving in a constant direction, whereas the circle is a
locus of a point moving at a constant distance from some
fixed point. The theoretical importance of the circle is
reflected in the number of amazing applications.
Some properties
of a circle
CIRCLE THEOREM 1
Angle At The Centre
What is the angle at the centre? The
angle at the centre is twice the angle
at the circumference of a circle. In the
diagram above, the two points B and
D on the circumference are joined to
the centre, C, and to another point on
the circumference, A.
Circle Theorem 2
Angles In The Semi Circle
(Thales' Theorem)
What are angles in the semicircle? Angles in a
semicircle are created when you join the two
ends of the diameter to one point on the arc
using cords. In the diagram below, A B AB is the
diameter of a circle that divides the circle into
two.
Circle Theorem 3
Angles In The Same
Segment
Angles in the same segment
are equal.
The angle in the
circumference subtended by
the same arc are equal. More
simply, angles in the same
segment are equal.
Circle Theorem 4
Cyclic Quadrilateral
A cyclic quadrilateral is a four sided shape
that can be inscribed into a circle. Each
vertex of the quadrilateral lies on the
circumference of the circle and is connected
by four chords. The opposite angles of a
cyclic quadrilateral have a˚ total of. 180˚
Circle Theorem 5
Radius To A Tangent
A line that touches the circle at
a single point is known as a
tangent to circle. The point
where tangent meets the circle
is called point of tangency. The
tangent is perpendicular to the
radius of the circle, with which
it intersects.