# Thread: Circle Geometry: Proving Parrallel Lines

1. ## Circle Geometry: Proving Parrallel Lines

Two circles intersects in X and Y. The tangent at X to the first circle cuts the second circle at A and AY produced cuts the first circle at B. Prove that XB is parallel to the tangent at A to the second circle.

2. Extend $AX$ we have $X$ being in the segment $AM$ therefore , $\angle MXB = \angle BYX$ Moreover , $\angle NAX = \angle AYX$ where $AN$ is the tagent to the second circle and $N$ and $B$ are in the opposite side .

By looking at line $AYB$ we obtain

$180^o = \angle BYX + \angle AYX = \angle MXB + \angle NAX$

$\angle AXB = \angle NAX$

3. Where is M located?

Sorry, isnt X a tangent? Producing AX will not render M on circle.

4. Ok nvm