Y by Adventure10, Mango247
As shown in the following figure, point
lies on the circumcicle of triangle
Lines
and
meet at
and lines
and
meet at
The perpendicular bisector of line segment
meets line segment
at
and the perpendicular bisector of line segment
meets line segment
at
Prove that
![\[ \left(\frac{CE}{BF} \right)^2 = \frac{AJ \cdot JE}{AK \cdot KF}.\]](//latex.artofproblemsolving.com/f/7/1/f71daec1c506efa43a4ab6352fcdc9a07dbf24b2.png)














![\[ \left(\frac{CE}{BF} \right)^2 = \frac{AJ \cdot JE}{AK \cdot KF}.\]](http://latex.artofproblemsolving.com/f/7/1/f71daec1c506efa43a4ab6352fcdc9a07dbf24b2.png)