Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Is a regular polygon of sides circumscribed about a circle of centre and radius
MATHEMATICS · Subjective · A Level · Mathematics · Vectors · Vectors
Problem
A
1
,
A
2
,
A
3
,
…
,
A
n
A_1,A_2,A_3,\dots,A_n
A
1
,
A
2
,
A
3
,
…
,
A
n
is a regular polygon of
n
n
n
sides circumscribed about a circle of centre
O
O
O
and radius
a
a
a
.
P
P
P
is any point at distance
c
c
c
from
O
O
O
. Show that the sum of the squares of the perpendiculars from
P
P
P
to the sides of the polygon is
n
(
a
2
+
c
2
2
)
n\left(a^2+\frac{c^2}{2}\right)
n
(
a
2
+
2
c
2
)
.
Related theory
Statics
Dot Product
Vectors
Scalar product
Vector Algebra
Dot product of two vectors
Browse the problem library