Given four points
![D](/media/m/7/0/0/7006c4b57335ab717f8f20960577a9ef.png)
on a circle such that
![AB](/media/m/5/2/9/5298bd9e7bc202ac21c423e51da3758e.png)
is a diameter and
![CD](/media/m/8/9/5/895081147290365ccae028796608097d.png)
is not a diameter. Show that the line joining the point of intersection of the tangents to the circle at the points
![C](/media/m/5/a/b/5ab88f3f735b691e133767fe7ea0483c.png)
and
![D](/media/m/7/0/0/7006c4b57335ab717f8f20960577a9ef.png)
with the point of intersection of the lines
![AC](/media/m/6/4/7/647ef3a5d68f07d59d84afe03a9dc655.png)
and
![BD](/media/m/1/1/f/11f65a804e5c922ee28a53b1df04d138.png)
is perpendicular to the line
%V0
Given four points $A,$ $B,$ $C,$ $D$ on a circle such that $AB$ is a diameter and $CD$ is not a diameter. Show that the line joining the point of intersection of the tangents to the circle at the points $C$ and $D$ with the point of intersection of the lines $AC$ and $BD$ is perpendicular to the line $AB.$