Convex quadrilateral
has
. Point
is the foot of the perpendicular from
to
. Points
to
lie on sides
and
, respectively, such that
lies inside triangle
and
Prove that line
is tangent to the circumcircle of triangle
.
%V0
Convex quadrilateral $ABCD$ has $\angle ABC = \angle CDA = 90^\circ$. Point $H$ is the foot of the perpendicular from $A$ to $BD$. Points $S$ to $T$ lie on sides $AB$ and $AD$, respectively, such that $H$ lies inside triangle $SCT$ and $$
\angle CHS - \angle CSB = 90^\circ, \quad
\angle THC - \angle DTC = 90^\circ \text{.}
$$
Prove that line $BD$ is tangent to the circumcircle of triangle $TSH$.
Školjka