Let
be a convex quadrilateral
and
a point inside it. The feet of the perpendiculars from
to
are
respectively. The feet of the perpendiculars from
to the sides of
, the quadrilateral
, are
, where
Prove that
is similar to S.
%V0
Let $S$ be a convex quadrilateral $ABCD$ and $O$ a point inside it. The feet of the perpendiculars from $O$ to $AB, BC, CD, DA$ are $A_1, B_1, C_1, D_1$ respectively. The feet of the perpendiculars from $O$ to the sides of $S_i$, the quadrilateral $A_iB_iC_iD_i$, are $A_{i+1}B_{i+1}C_{i+1}D_{i+1}$, where $i = 1, 2, 3.$ Prove that $S_4$ is similar to S.
Školjka