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The late mathematician Cezar Cosnita, using the barycentre coordinates, proves two theorems which are the subject of this article. In a remark made after proving the first theorem, C. Cosnita suggests an elementary proof by employing the concept of polar. In the following, we prove the theorems based on the indicated path, and state that the second theorem is a particular case of the former. Also, we highlight other particular cases of these theorems.doi:10.5281/zenodo.30253 fatcat:bqytk4fgk5fnre7mk3cu7bthxa