Geometry+ 05: UNIZOR.COM - Math+ &Problems - Geometry
Channel: Zor Shekhtman on UNIZOR Education
Date: 2024-02-04

UNIZOR.COM - Creative Mind through Art of Mathematics
Read full text of notes for this lecture on UNIZOR.COM - Math+ &Problems - Geometry - Geometry 05.

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Geometry+ 05


Problem A

Construct a quadrilateral ABCD by its 4 sides AB, BC, CD, DA and an angle φ between opposite sides AB and CD.


Problem B

Given a circle of radius R and n-sided regular polygon inscribed into it.
Let P be any point on this circle.
Find a sum of squares of distances from this point P to all vertices of a polygon.


Problem C

Given an equilateral triangle ΔABC.
Extend side AC beyond vertex C to point D and build another equilateral triangle CDE with point E on the same side from AD as point B.
Connect points A and E. Let point M be a midpoint of segment AE.
Connect points B and D. Let point N be a midpoint of segment BD.
Prove that triangle ΔCMN is equilateral.