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Quadrilaterals,
Polygons - Regular Polygons, Circle |
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Circle
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Central angle, inscribed angle
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Construction of a tangent
from a point
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Circumference, length of an arc
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Circle and circular sector
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Circular segment
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Annulus and annulus segment |
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Circle
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A circle is a set of points that are at the fixed distance (called the
radius r) from a fixed point called the center
O. |
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Central angle, inscribed angle
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A
central angle is
double the inscribed angle (formed when two secant lines intersect
on the circle) subtended by the same arc. |
Proof:
Angles
b1
and b2 are
external angles of the isosceles triangles AOC and
BOC, hence |
b1
= 2a1,
b2
= 2a2,
a
= a1+
a2
=>
b = b1+
b2
= 2(a1+
a2)
= 2a |
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Inscribed angles
subtended by the same arc are equal. An angle inscribed in a semicircle is a right angle. |
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Construction of a tangent
from a point P
to a circle c. |
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The
midpoint of the line segment OP
is the circumcenter of the quadrilateral PD1OD2.
The lines PD1
and PD2
are tangents from P
to the given circle c. |
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Circumference, the length of a circle - the perimeter:
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Length of an arc:
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Circle and circular sector
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By substituting
P = 2pr
and R
= r
in the formula for the area of a regular polygon, obtained is the formula
for the area of a circle, that is : |
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Circular segment
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The portion of a circle bounded by an arc and a chord is called a segment. |
Symbols
used in the formulas: c
-chord, r
-radius, h
-height of a segment, A
-area of a segment. |
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Annulus and annulus segment |
Annulus
or ring is the region enclosed between two concentric circles. |
Annulus |
Annulus
segment |
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Geometry
and use of trigonometry contents - A |
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