Quadrilateral ABCD

Quote:

Originally Posted by disclaimer

Quadrilateral $ABCD$ is inscribed in a circle, where the tangents to this circle at points $B$ and $D$ intersect on the straight line joining $A$ and $C$ . Show that:

$AB\cdot{CD}=AD\cdot{BC}$

Thanks in advance.

If P is the point of intersection of two tangents at B and D and the line CA, then
PB = PD. You can easily show that the triangles PBA and PBD are congruent. Similarly Triangles PBC and PDC arfe also congruent.
Now proceed further to get the required result.