1) The document discusses plane sections of a sphere, which are the intersections of a plane and a sphere at common points. 2) It provides the equation of a sphere centered at the origin with radius r, and defines a point C(a,b,c) at the center of the plane section. 3) Any point P(x,y,z) on the plane section must satisfy the condition of perpendicularity between the line segments OP and OC, resulting in an equation relating the coordinates of P.

1. Presentation By Vamshi TG

2. Consider a plane and a Sphere ,we suppose that sphere and
plane have points in common i.e. the interception of sphere and
plane at these set of common points is called Plane section
of a Sphere.

5. T h e e q u a t i o n o f t h e
s p h e r e w i t h o r i g i n a s
c e n t r e a n d r a d i u s r i s
g i v e n b y
x 2 + y 2 + z 2 =r 2
.....(i )
L e t C (a , b , c ) b e t h e
c e n t r e o f t h e p l a n e
s e c t i o n o f t h e s p h e r e
w h o s e e q u a t i o n w e
h a v e t o f i n d o u t . T h e
l i n e s e g m e n t O C d r a w n

6. L e t P (x ,y ,z ) b e a n y p o i n t o n t h e
p l a n e s e c t i o n .
T h e d i r e c t i o n r a t i o o f P C a r e x -
a , y - b ,z - c a n d i t i s p e r p e n d i c u l a r
t o O C .
U s i n g t h e c o n d i t i o n o f
p e r p e n d i c u l a r i t y , w e h a v e
( x - a ) a + ( y -b ) b +( z -c ) c =0 ....(i i )
E q u a t i o n (i i ) i s s a t i s f i e d b y t h e
c o -o r d i n a t e s o f a n y p o i n t P o n t h e

7. Great circle is also known
as orthodrome or Riemannian circle.
•Definition Of Great circle: A great circle of a sphere is
the intersection of the sphere and a plane which passes
through the center point of the sphere.

8. Small circle of a sphere is defined as the
intersection of a sphere and a plane, If the plane
does not pass through the center of the sphere