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4

Part of 2016 Oral Moscow Geometry Olympiad

Problems(2)

right triangle and excircle given, collinear wanted

Source: 2016 Oral Moscow Geometry Olympiad grades 8-9 p4

7/30/2019
Let MM and NN be the midpoints of the hypotenuse ABAB and the leg BCBC of a right triangles ABCABC respectively. The excircle of the triangle ACMACM touches the side AMAM at point QQ, and line ACAC at point PP. Prove that points P,QP, Q and NN lie on one straight line.
geometryright triangleexcirclecollinear
for which n convex n-gonal prism with equal sides is a right one

Source: 2016 Oral Moscow Geometry Olympiad grades 10-11 p4

7/29/2019
In a convex nn-gonal prism all sides are equal. For what nn is this prism right?
geometry3D geometryprism