Two similar triangles ABC and EBD. Two line segments meet at point F. Prove that ABFC and EBDF are cyclic quadrilaterals.

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## Solution

ΔABC∽ΔEBD

AB:BE=BC:BD

ΔABE∽ΔCBD

∠BAE=∠BCD, ABFC cyclic

∠AEB=∠CDB, EBDF cyclic