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Let be a chord of a circle with centre
MATHEMATICS · Subjective · CBSE · Mathematics · Circles · Circles
Problem
Let
A
B
AB
A
B
be a chord of a circle with centre
O
O
O
. The line
O
P
OP
O
P
meets
A
B
AB
A
B
at its midpoint
P
P
P
. (a) Prove that
O
P
OP
O
P
is perpendicular to
A
B
AB
A
B
. (b) Another chord
C
D
CD
C
D
is drawn such that
O
P
⊥
C
D
OP\perp CD
O
P
⊥
C
D
at
Q
Q
Q
. Prove that
C
Q
=
Q
D
CQ=QD
C
Q
=
Q
D
. (c) If
A
B
=
18
cm
AB=18\,\text{cm}
A
B
=
18
cm
and
O
A
=
11
cm
OA=11\,\text{cm}
O
A
=
11
cm
, find
O
P
OP
O
P
.
Related theory
Pythagoras' Theorem
Triangle Properties
Chord Properties
Circles
Perpendicular from centre to a chord
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