MathDB

Quadrilateral

ABCD

with perpendicular diagonals is inscribed in a circle with centre

O

. The tangents to this circle at

A

and

C

together with line

BD

form the triangle

\Delta

. Prove that the circumcircles of

BOD

and

\Delta

are tangent.
[hide=Additional information for Junior League]Show that this point lies belongs to

\omega

, the circumcircle of

OAC

Proposed by A. Kuznetsov

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