The document discusses key concepts relating to circles such as: 1) The perimeter of a circle is 2πr, where r is the radius of the circle. 2) An arc is part of a circle, and the central angle of an arc is the angle formed by the endpoints of the arc and the center of the circle. 3) The area of a circle can be calculated as πr^2, where r is the radius.

1. Circular
MEASURES
STANDARD 9

4. r
Perimeter of a circle is
2пr
П ≈3.141

5. A
B
AB is part of the circle ,it is known as Arc

6. A
B
O
The angle made by joining the end points of an arc to
the center of the circle is called the central angle of
an arc.
Eg: angle AOB is the central angle of the arc AB

7. For an arc of central angle x°,
arc length =2пr × x/360
r = radius of the circle

8. If we draw regular polygons with more
and more sides within the circle, their
areas would get closer and closer to
the area of the circle.

9. By joining the vertices of the polygon to the center
of the circle, we can divide the polygon into
triangles
The area of the polygon is the sum of the
areas of these triangles; and all these triangles
are congruent. So we need only multiply the
area of one triangle by the number of triangle.

10. To find the area of the
Dtrriaawn gtlhee perpendicular from the center of the
circle to a side of the polygon
h
s
Area of the triangle is
½ × s × h = 1/2sh

11. If the polygon has n sides, then
its area is
n × 1/2 × sh = ½ n s h
n s is the sum of all sides of
the polygon ie. Perimeter so we
can denote p= ns
Therefore ,
Area of the Polygon =
½ ph

12. Thus as the number of sides of the
polygon increases, in the area
½ ph of the polygon, the perimeter gets
closer and closer to the perimeter of
the circle and the perpendicular
distance h gets closer and closer to the
radius of the circle.
Thus
area of the circle = ½ × perimeter of
the circle
× radius

13. Area of the circle =1/2 × 2п× radius (r)× radius
= п푟2