MathDB

3D geo with n circles having a common point

Source: St Petersburg 2021 11.3

December 23, 2021

geometry3D geometrypyramidcircumcircle

Problem Statement

In the pyramid

SA_1A_2 \cdots A_n

, all sides are equal. Let point

X_i

be the midpoint of arc

A_iA_{i+1}

in the circumcircle of

\triangle SA_iA_{i+1}

for

1 \le i \le n

with indices taken mod

n

. Prove that the circumcircles of

X_1A_2X_2, X_2A_3X_3, \cdots, X_nA_1X_1

have a common point.

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