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
