Important: I NEED HELP WITH A QUESTION......please help me its so frustrating arrgh!! (1 Viewer)

[MandiMoo]

Hey my techer photocopied some questions for me and they dont have answers!!! I need someone to answer this question for me, its a 'geometry of the circle' question i have drawn the diagram and can match up a few angles but nothing that leads to anything. Here it is:

"P is the midpoint of a chord AB of a circle. XY is a chord containing the point P. The tangents at X and Y meet AB extended at M and N respectively. Prove that AM = BN."

I would add a pic of the diagram to make it a little easier for the real nice people who try and help me, but i dont know how to do that either!

Please help I'm going to burst from frustration!!! :S:S:S

 

[shafqat]

The answer involves proving triangles ANY and BMX are congruent by SAS, which you get through isos trianges and alt segment theorem. Could someone try to write it out, because I'm a little busy atm.

 

[Lunatic]

I don't think it's through isos because P isn't the mid-point of XY, XY just passes through it. Hang on, I'm working on it now; even if I don't get the answer I'll post up what I did.

...okay, all I managed to do was prove that triangle APX is similar to triangle PBY, and the alternating sides AP and PB were equal. I'm not sure if this helps with the question at all.

 

[lum]

damn couldn't work it out, i only got to what lunatic got..

 

[polythenepam]

okay heres a solution i attached, im not sure if its the quickest way though...
i left out the obvious steps because i figured it would take too much space. Ok have fun!

 

[who_loves_maths]

^ wow, what elegance and perception... wish i'd have thought of that method when i tried to do it

nice work poly.