The document covers fundamental concepts of circle geometry, including properties of angles formed by diameters and chords. It states that angles made by a diameter on the circumference are 90 degrees, and that a tangent is perpendicular to the radius at the point of contact. Additionally, it highlights the equality of segments created by a perpendicular from the center to a chord and mentions further resources for learning.

1. WELCOME TO THE
PRESENTATION

2. CIRCLE GEOMETRY
B
C
D
E
A
All angles made by
diameter on the
circumference of circle
are 90 degree.
 Angle ABD = 90
 Angle ACB = 90
 Angle AEC = 90
A B
CD
All angles made by a chord on
the circle are equal.
 Angle ACB = Angle BDA
T
P
R Q
B
O
C
A
Φ
Φ
2Φ
Φ
 Angle TPR = Angle PQR  Angle BOQ =2×angle BAC

3. B
C
A
A
 Exterior Angle A = angle C
 A+C = 180
 B+D = 180
Φ
Φ
B
P
PA = PB
CIRCLE GEOMETRY
D

4. P
Q
T
PA = PB
O
Angle PTQ = 2 × Angle OPQ
P
Q
T
PA = PB
+ = 180 degree
+ = 360 degree
= 2
CIRCLE GEOMETRY

5. o
BP
90
If in a circle a perpendicular is
drawn from center to a chord
then it divides it in two equal
halves.
OD perpendicular to AB at D
Then AD=DB
D
B
Q
P
PQ×PQ = PB×PA
A
Tangent drawn on the
circumference of a circle is
perpendicular to the line drawn
for the center of that circle
90
CIRCLE GEOMETRY

6. M
If AC=BC=AB and r is the radius of
both the circles
Then, CD= 2 r & AM=MB= r
O BA
P
Circle with single common tangent
By property of tangent in figure
OP=OA &OP=OB
Therefore AO=OB
CIRCLE GEOMETRY

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