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In a circle with centre
MATHEMATICS · Multi-part · CBSE · Mathematics · Circles · Circles
Problem
In a circle with centre
O
O
O
, a chord
A
B
AB
A
B
is drawn. (i) Prove that if
O
P
⊥
A
B
OP\perp AB
O
P
⊥
A
B
, then
A
P
=
P
B
AP = PB
A
P
=
P
B
. (ii) Conversely, prove that if a point
P
P
P
on
A
B
AB
A
B
is such that
A
P
=
P
B
AP = PB
A
P
=
P
B
, then
O
P
⊥
A
B
OP\perp AB
O
P
⊥
A
B
.
Related theory
Triangle Congruence
Chord Properties
Circles
Perpendicular from centre to a chord
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