A Proof of Congruent Circumcircles
Triangle ABC is constructed (Figure 1) using The Geometer’s Sketchpad©.
A tool for construction of the orthocenter (Assignment 5) is used to construct the
orthocenter, H. Segments
The circumcenter, O is constructed by a tool (Assignment 5), and given in Figure 3 with segments connecting it to the three vertices of the triangle.
The circumcircle for
We then use our tools to construct the
circumcenter, O’ and circumcircle (red) of
At this point we hypothesize that the
We first construct the segments,
Now since AC is a shared side of
Figure 7: O and O’ both lie on the
perpendicular bisector of
Quadrilateral COAO’ is formed by segments CO, OA, AO’ and
O’C. The diagonals of the quadrilateral are AC and OO’. Since
Figure 8: The circumcircles for
Download Assign08KM.gsp to explore this problem.
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