TUYMAADA 2018 Problem 8

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.

Proposed by A. Kuznetsov