My problem is:
$AB$ is a diameter of a circle and $BM$ is the tangent at $B$. If the tangent at $C$ on the circle meets $BM$ at $X$ and if $AC$ produced meets $BM$ at $Y$, prove $BX=XY$.
And this was how I approached, In the figure, we join $B$ to $C$ to have angle $ACB$ equal to $90^{\circ}$. and see that $XB=XC$. Also, that angle $ABY$ equals to $90^{\circ}$.
But, I am not able to have $XY$ anywhere. All, I see and have is a few angles and as sides only radii and the above relation between $XB$ and $XC$.
If anybody could tell me how can I have $XY$ or anything related to that in my solution or any other way to approach this problem, (I would prefer this rather than solution) I will really appreciate that.