Abstract
In this paper we investigate some properties related to the Brocard circle of a given triangle ∆ABC. Four of them correspond to the special point of a triangle that satisfies some conditions. Another one corresponds to the special case of ∆ABC for which the relation \( ({\text{AC}}^{2} + {\text{AB}}^{2} )/2 = {\text{BC}}^{2} \) holds. We analyzed the case where a symmedian is a tangent to the Brocard circle. We found some interesting properties related to the Brocard circle for right angle triangle and for isosceles triangle.
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References
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Oxman, V., Sigler, A., Stupel, M. (2019). The Properties of Special Points on the Brocard Circle in a Triangle. In: Cocchiarella, L. (eds) ICGG 2018 - Proceedings of the 18th International Conference on Geometry and Graphics. ICGG 2018. Advances in Intelligent Systems and Computing, vol 809. Springer, Cham. https://doi.org/10.1007/978-3-319-95588-9_29
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DOI: https://doi.org/10.1007/978-3-319-95588-9_29
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