Given **AC**, **CB**, **AD**, **DB** such that
**AC + CB = AD + DB**.

Extend **AC** and **DG** to intersect at point **X**.

Extend **AD** and **CG** to intersect at point **Y**.

Prove that **AX + XB = AY + YB.**

If we consider points

AandBas the foci of an ellipse, then by the definition of an ellipse, that it is the locus of points with distances from two foci a constant sum, then pointsCandDare points on the ellipse.Does this help? Is there any argument that points X and Y will be points on an ellipse with focal points

AandB?

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