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Tuymaada Olympiad
2001 Tuymaada Olympiad
6
6
Part of
2001 Tuymaada Olympiad
Problems
(1)
(AC=BC, P,Q in AB): <PCQ \le <ACB /2 => PQ\le AB/2
Source: Tuymaada Junior 2001 p6
4/30/2019
On the side
A
B
AB
A
B
of an isosceles triangle
A
B
AB
A
B
(
A
C
=
B
C
AC=BC
A
C
=
BC
) lie points
P
P
P
and
Q
Q
Q
such that
∠
P
C
Q
≤
1
2
∠
A
C
B
\angle PCQ \le \frac{1}{2} \angle ACB
∠
PCQ
≤
2
1
∠
A
CB
. Prove that
P
Q
≤
1
2
A
B
PQ \le \frac{1}{2} AB
PQ
≤
2
1
A
B
.
geometry
geometric inequality
isosceles
Isosceles Triangle