Geometry | NMTC sub junior | Equilateral Triangle | Mathematical Olympiad | Congruence | Cyclic

Описание: This problem can be used to practice for IMO, IOM, UIMO, PRMO, RMO, IOQM, JMO, NMTC and other Mathematical Olympiad.

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A straight line l is drawn through the vertex C of an equilateral triangle ABC, wholly lying outside the triangle. AL, BM are drawn perpendiculars to the straight line l. If N is the midpoint of AB, prove that triangle LMN is an equilateral triangle.
NMTC - (National Mathematics Talent Contests)
Sub Junior Final Round-2023

This is Very nice Geometry problem from 2023, NMTC sub junior, for those who are preparing for different Mathematical Olympiads. Different concept of parallelogram and its area is being used in this problem. In this Question congruence of triangle and concept of cyclic quadrilateral is beautifully used.

This problem will increase your the observation in geometrical figures and build up the concept which are used in Olympiads.
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