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maximum of sin CAT +sin CBT if T centroid m <TAB = <ACT

Source: Czech and Slovak Match 1998 P5

October 1, 2017
maximum valuetrigonometryequal anglesCentroidgeometry

Problem Statement

In a triangle ABCABC, TT is the centroid and ∠TAB=∠ACT \angle TAB = \angle ACT. Find the maximum possible value of sin∠CAT+sin∠CBTsin \angle CAT +sin \angle CBT.
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