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Contents
Angle Properties
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Angle Properties of Circle
Property 1 An angle at the centre of a circle is twice any angle at the circumference subtended by the same arc. Proof: In the figure below, the angles are subtended by the minor arc AB. Since OA
= OD (radii of circle), a = b (base angles of isos.
triangle)
But
angle AôE if the exterior angle of triangle AOD
AôE =
2a
Similarly,
c = d (base angles of isos. triangle)
BôE =
2c
Hence,
AôB = 2a + 2c = 2(a + c) = 2 angle ADB
Property
1 can be abbreviated as Ð
at
centre= 2Ðat
⊙ce
Property 2
Every
angle at the circumference subtended by the diameter of a circle is a right
angle triangle.
Property
2 can be abbreviated as
rt. Ðin a
semicircle.
Proof
 AôB =
2AĈB
( at centre = 2 at )
But AôB
= 180°
AĈB
= 90°
Property
3
Angles
in the same segment of a circle are equal.
Proof
 AôB =
2x1 = 2x2 (Ð at
centre= 2Ðat
⊙ce)
x1
= x2
ÐAPB
= ÐAQB
Property
3 can be abbreviated as Ðs
in the same segment.
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