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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 triangle's 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 |
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| Copyright
© 2004 - 2012, Nabla Ltd. All rights reserved. |
