MathDB

2023 CUBRMC Proof #4 ain't no sunshine without geo (orthodiagonal quad)

Source:

March 8, 2024

geometrytangentialcubrmc

Problem Statement

Let square

ABCD

and circle

\Omega

be on the same plane, and

AA'

BB'

CC'

DD'

be tangents to

\Omega

. Let

WXY Z

be a convex quadrilateral with side lengths

WX = AA'

XY = BB'

Y Z = CC'

, and

ZW = DD'

. If

WXY Z

has an inscribed circle, prove that the diagonals

WY

and

XZ

are perpendicular to each other.