MathDB

2

Part of 2011 Oral Moscow Geometry Olympiad

Problems(2)

angle chasing inside an isosceles triangle, equal segments and right angle

Source: 2011 Oral Moscow Geometry Olympiad grades 8-9 p2

4/17/2020
In an isosceles triangle ABCABC (AB=ACAB=AC) on the side BCBC, point MM is marked so that the segment CMCM is equal to the altitude of the triangle drawn on this side, and on the side ABAB, point KK is marked so that the angle ∠KMC\angle KMC is right. Find the angle ∠ACK\angle ACK.
anglesgeometryisoscelesequal segmentsright angle
2011 lines equidistant from line and not intersecting it, plane related

Source: 2011 Oral Moscow Geometry Olympiad grades 10-11 p2

4/7/2020
Line ℓ\ell intersects the plane aa. It is known that in this plane there are 20112011 straight lines equidistant from ℓ\ell and not intersecting ℓ\ell. Is it true that ℓ\ell is perpendicular to aa?
3D geometrygeometrylinesPlane