Let
be a triangle.
is a point on the side
. The line
meets the circumcircle again at
.
is the foot of the perpendicular from
to
, and
is the foot of the perpendicular from
to
. Show that the line
is a tangent to the circle on diameter
if and only if
.
%V0
Let $ABC$ be a triangle. $D$ is a point on the side $(BC)$. The line $AD$ meets the circumcircle again at $X$. $P$ is the foot of the perpendicular from $X$ to $AB$, and $Q$ is the foot of the perpendicular from $X$ to $AC$. Show that the line $PQ$ is a tangent to the circle on diameter $XD$ if and only if $AB = AC$.
Školjka