A right-angled triangle
has its right angle at the point
An arbitrary circle with center on the line
is tangent to the line
Let
be the tangent to the circle different from
(
is the point of tangency). Prove that the median from
of the triangle
intersects
at a point
such that
%V0
$(FRA 4)$ A right-angled triangle $OAB$ has its right angle at the point $B.$ An arbitrary circle with center on the line $OB$ is tangent to the line $OA.$ Let $AT$ be the tangent to the circle different from $OA$ ($T$ is the point of tangency). Prove that the median from $B$ of the triangle $OAB$ intersects $AT$ at a point $M$ such that $MB = MT.$
Školjka