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minimum distance of a walk of an ant on a specific pyramid

Source: May Olympiad (Olimpiada de Mayo) 1995 L2

September 12, 2018

geometrypyramidminimumdistance3D geometry

Problem Statement

Consider a pyramid whose base is an equilateral triangle

BCD

and whose other faces are triangles isosceles, right at the common vertex

A

. An ant leaves the vertex

B

arrives at a point

P

of the

CD

edge, from there goes to a point

Q

of the edge

AC

and returns to point

B

. If the path you made is minimal, how much is the angle

PQA