Let two points interior to the circle such that is the midpoint of Let an arbitrary point lies on and the second intersections of the lines with respectively. The tangents in with respect to the circle intersect each other at Prove that the perpendicular bisector of the segment passes through the midpoint of
Sorry, I don’t know how to post figure, I hope you can draw the figure yourself.
My Solution: J is midpoint of line segment SI and the intersection of and circle is Q.
Since the above things, we have . So we done if we proof that .
Because is the midpoint of the line segment so is a parallelogram => =
Ong The Phuong said
Sorry, I don’t know how to post figure, I hope you can draw the figure yourself.
and circle 
is Q.
My Solution: J is midpoint of line segment SI and the intersection of
Since the above things, we have
. So we done if we proof that 
.
Because
is the midpoint of the line segment 
so 
is a parallelogram => 
= 
=>
=> 
(because 
)
In the order hand,
, 
hence 
. we done.