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International Contests
Czech-Polish-Slovak Match
1998 Czech and Slovak Match
5
5
Part of
1998 Czech and Slovak Match
Problems
(1)
maximum of sin CAT +sin CBT if T centroid m <TAB = <ACT
Source: Czech and Slovak Match 1998 P5
10/1/2017
In a triangle
A
B
C
ABC
A
BC
,
T
T
T
is the centroid and
∠
T
A
B
=
∠
A
C
T
\angle TAB = \angle ACT
∠
T
A
B
=
∠
A
CT
. Find the maximum possible value of
s
i
n
∠
C
A
T
+
s
i
n
∠
C
B
T
sin \angle CAT +sin \angle CBT
s
in
∠
C
A
T
+
s
in
∠
CBT
.
maximum value
trigonometry
equal angles
Centroid
geometry