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right angle wanted, tangents, angle bisector related

Source: Tuymaada Junior 2003 p7

May 11, 2019
geometryangle bisectorTangentsperpendicular

Problem Statement

Through the point K K lying outside the circle ω \omega , the tangents are drawn KB KB and KD KD to this circle (B B and D D are tangency points) and a line intersecting a circle at points A A and C C . The bisector of angle ABC ABC intersects the segment AC AC at the point E E and circle ω \omega at F F . Prove that ∠FDE=90∘ \angle FDE = 90^\circ .
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