A PowerPoint presentation on circles defines key terms like diameter, radius, circumference, chord, tangent, and sectors. It presents a theorem stating that for any external point, the lengths of the two tangents drawn to a circle are equal, and the angles between each tangent and the line segment joining the point to the circle's center are also equal. A proof of the theorem is provided using properties of congruent triangles.

1. A
POWERPOIN
PRESENTATION
ON
CIRCLE

2. What is a circle?
• Circles are simple closed curves which
divide the plane into two regions: an
interior and an exterior.

3. Features OF
CIRCLE…….
… the distance from
… the distance
… the distance the
the centre of across
the circle,any Circle…
around the
circle to passing
point
Diameter through the centre of
on the
… its PERIMETER
the circle
circumference
Radius

4. Minor Major
Segment Segment
C
AR
… part of the touches
a line which two
joining
d
circumference of a at
points on the
the circumference
or
Ch
circle
circumference.
one point only
… chord divides circle
From Italian tangere,
to touch segments
into two
Tan
g en
t

5. Major sector
SECANT
Minor Sector

6. TANGENT
A tangent to a circle is a
line that intersects the
circle at only one point A
B

7. A tangent is
perpendicular
to the radius
of a circle

8. THEOREM
THE LENGTH OF TWO TRIANGLES TO A CIRCLE
FROM A EXTERNA POINT A EQUA A THEY
N L RE L ND
A EQUA INCLINED TO THE LINE SEGMENT
RE LLY
JOINING THE CENTRE A THA POINT
T T

9. GIVEN: In c(o , r),tangents AP, PB
Are shown from the external point P.
To prove: AP=PB, APO= BPO
Const.: join AO & BO
Proof: In,
∆AOP=∆BOP
OP=OP (common)
OAP=OBP (Each 90°)
AO=OB (radii of same circle)
∆AOP =~ ∆BOP (R.H.S)
AP=PB, APO= BPO C.P.C.T
HENCE PROVED…..