Presentation By Vamshi TG

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.

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

f r o m O t o t h e p l a n e

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

p l a n e . H e n c e (i ) a n d (i i ) t o g e t h e r

Great circle is also known as orthodrome or Riemannian circle.

•Definition Of Great circle: A great circle of a sphere isthe intersection of the sphere and a plane which passes through the center point of the sphere.

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