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National and Regional Contests
India Contests
India National Olympiad
1998 India National Olympiad
1
1
Part of
1998 India National Olympiad
Problems
(1)
Yet another circle!
Source: INMO 1998 Problem 1
10/6/2005
In a circle
C
1
C_1
C
1
with centre
O
O
O
, let
A
B
AB
A
B
be a chord that is not a diameter. Let
M
M
M
be the midpoint of this chord
A
B
AB
A
B
. Take a point
T
T
T
on the circle
C
2
C_2
C
2
with
O
M
OM
OM
as diameter. Let the tangent to
C
2
C_2
C
2
at
T
T
T
meet
C
1
C_1
C
1
at
P
P
P
. Show that
P
A
2
+
P
B
2
=
4
⋅
P
T
2
PA^2 + PB^2 = 4 \cdot PT^2
P
A
2
+
P
B
2
=
4
⋅
P
T
2
.
geometry
india