$O$ is the centre of the large circle
$AB$ is a chord of the large circle
$OB$ is a diameter of the small circle.
Both circles touch at $B$
The small circle cuts the chord $AB$ at $X$
prove that $AX = XB$
I made $OB$ and $AO$ into lines which created an isosceles triangle (because $O$ is the midpoint). I think the next step is to make a line to bisect it, but how would I know where to draw the line?