PROPERTIES OF CIRCLE
WHAT IS CIRCLE?
- circle is the locus of all points equidistant form a central point.
HOW ABOUT THE DEFINITION OF TERMS?
- ORIGIN = THE CENTER OF CIRCLE.
- RADIUS=THE DISTANCE FORM CENTER TO ANY POINT OF CIRCLE.
- CHORD=A LINE SEGMENT WITHIN A CIRCLE THAT TOUCH ANY TWO POINTS ON THE CIRCLE.
- DIAMETER=THE LONGEST CHORD THAT PASS TO THE CENTER OF THE CIRCLE.
- ARC= THE PAST OF CIRCUMFERENCE OF THE CIRCLE.
- SECTOR=THE AREA OF THE CIRCLE FORMED BY CONNECTING TWO RADIUS AND ARC CALLED A SECTOR.
- SEGMENT=REGION BOUNDED BY A CHORD AND ARC OF THE CIRCLE IS CALLED SEGMENT.
Properties of Circle
Property 1 ( Property of isosceles
triangle)
If we join end point of a chord to the
center of circle
Then an isosceles is fromed. The
base angles are equal
As in the figure below.
Property 2 (angles in semicircle)
The angle inscribed in semicircle is
always 90 degree
Property 3 (central angle and inscribed
angle)
The angle subtended by the central angle
is twice
the inscribed angle subtended the same
arc.
Property 4 (perpendicular bisector of a
chord)
Properties bisector of a chord always
pass through
The center. In otherworld’s the
perpendicular line
from the center of the circle to the
chord always bisects the chord.
Property 5 (equal chord)
In the same circle two chords are same if
and only if they are equidistant from the center
Property 6 (Tangent and radius)
Tangent of circle always perpendicular to
the radius
Property 7 (Two tangent of circle )
Tangent
to a circle from an external point are equal in length.
Property 8 (subtended angles from the
same arc)
Inscribed angles from the same arc are
equal.
In otherworld’s angles in the same
segment of the a circle
Are
equal
Property 9 (Angles in a cyclic
quadrilateral)
The sum of opposite angle in cyclic
quadrilateral
Is 180.
Property 10 (Alternative segment theorem)
Angle between a tangent and a chord is equal to the angle
Subtended by the same chord.
Property 11 (Intersecting chords)
For
any two interesting chords like AC and BC
AB*BC* = DB*BE
Property 12 (Tangent secant theorem)
AB is a tangent and BC is a secant of the
circle
O The property says that
Property 13 (Tangent secant theorem)
Total length * length out the circle
= Total length *length out side the
circle
"HARD WORKING IS THE WAY TO SUCCESS"
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