Saturday

August 30, 2014

August 30, 2014

Posted by **Bobby** on Sunday, July 20, 2008 at 8:51pm.

I believe the first step is to prove ABXY is a cyclic quadrilateral. Unfortunately, I dont know how!!!

- Maths -
**Reiny**, Sunday, July 20, 2008 at 9:24pmlet AX and BY intersect at D

since angle AXC = angle BYC

angle BXA = angle AYB (supplementary angles)

also since BX = XY

then

angle XBY = XYB (isosceles triangles) mark that angle o

now in triangles BXD and ADY you have opposite angles equal and angle BXA = angle AYB (see above)

so the third angle pair must be equal (supplementary angles)

then angle XBD = angle YAX = o

so now you have equal angles XBD and YAX subtended by XY

Therefore ABXY is a cyclic quadrilateral (properties of a cyclic quad)

then by the same cyclic quad properties

angles BAX and BYX are subtended by the same side BX in that cyclic quad.

Therefore angles BAX and BYX are equal, marked as o

QED !

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