Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
In a circle with centre
MATHEMATICS · Multi-part · CBSE · Mathematics · Circles · Circles
Problem
In a circle with centre
O
O
O
, chord
P
Q
PQ
P
Q
is such that a point
M
M
M
on
P
Q
PQ
P
Q
satisfies
P
M
=
M
Q
PM = MQ
P
M
=
M
Q
. (a) Prove that
O
M
OM
O
M
is perpendicular to
P
Q
PQ
P
Q
. (b) Hence, write the measure of
P
M
PM
P
M
in terms of the radius
r
r
r
and the distance
O
M
=
d
OM = d
O
M
=
d
.
Related theory
Pythagoras' Theorem
Triangle Properties
Chord Properties
Circles
Perpendicular from centre to a chord
Browse the problem library