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Circumcenter, Circumcircle and Centroid of a Triangle

Roland Coghetto (2016)

Formalized Mathematics

We introduce, using the Mizar system [1], some basic concepts of Euclidean geometry: the half length and the midpoint of a segment, the perpendicular bisector of a segment, the medians (the cevians that join the vertices of a triangle to the midpoints of the opposite sides) of a triangle. We prove the existence and uniqueness of the circumcenter of a triangle (the intersection of the three perpendicular bisectors of the sides of the triangle). The extended law of sines and the formula of the radius...

Čo s nejednoznačným zadaním slovnej úlohy?

Matúš Harminc, Jana Chudá (2016)

Učitel matematiky

In the paper we deal with a task about two circles touching in a rectangle. The assignment of the task was formulated in a fuzzy way, so solvers understood it differently. We present extracts from the authentic solutions which reflect this phenomenon. We suggest an approach to such tasks, how to solve them and how to assess their solutions.

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