929Mathematics Magazine, Problem 1671, proposed by M. N. Desh-
pande, Institute of Science, Nagpur, India
LetTbe the set of trianglesABCfor which there is a pointDonBC
such that segmentsAB,BD,AD,DC, andAChave integral lengths
and∠ACD=^12 ∠ABC=^13 ∠ADB.
(a) Characterize the sets{a, b, c}that are sets of side lengths of trian-
gles inT.
(b) Find the triangle of minimum area inT.