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angles of convex octagon wanted, squares inscribed and circumscribed in circle

Source: TOT 443 1995 Spring O J3 - Tournament of Towns

June 12, 2024

geometrySquaresangles

Problem Statement

Suppose

L

is the circle inscribed in the square

T_1

, and

T_2

is the square inscribed in

L

, so that vertices of

T_1

lie on the straight lines containing the sides of

T_2

. Find the angles of the convex octagon whose vertices are at the tangency points of

L

with the sides of

T_1

and at the vertices of

T_2

.
(S Markelov)