Let
be a trapezoid with parallel sides
. Points
and
lie on the line segments
and
, respectively, so that
. Suppose that there are points
and
on the line segment
satisfying
and
. Prove that the points
,
,
and
are concylic.
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Let $ABC$ be a trapezoid with parallel sides $AB > CD$. Points $K$ and $L$ lie on the line segments $AB$ and $CD$, respectively, so that $\frac {AK}{KB} = \frac {DL}{LC}$. Suppose that there are points $P$ and $Q$ on the line segment $KL$ satisfying $\angle{APB} = \angle{BCD}$ and $\angle{CQD} = \angle{ABC}$. Prove that the points $P$, $Q$, $B$ and $C$ are concylic.
Školjka