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Right angled triangle: IE=IF

Source: RMO Hyderabad 2016 , P1.

October 11, 2016
geometryincenter

Problem Statement

Let ABCABC be a right angled triangle with ∠B=90∘\angle B=90^{\circ}. Let II be the incentre of triangle ABCABC. Suppose AIAI is extended to meet BCBC at FF . The perpendicular on AIAI at II is extended to meet ACAC at EE . Prove that IE=IFIE = IF.
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