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find pyramid side ratios

Source: Yugoslav TST 1995 P3

May 27, 2021

geometry3D geometrypyramidratio

Problem Statement

Let

SABCD

be a pyramid with the vertex

S

whose all edges are equal. Points

M

and

N

on the edges

SA

and

BC

respectively are such that

MN

is perpendicular to both

SA

and

BC

. Find the ratios

SM:MA

and

BN:NC

.

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