Question

in figure, AE bisects angle BAD and AF bisects.angle CAD and AE perpendicular to AF.show that B,A,C are collinear

Answer 1

AE bisects ∠BAD

AF bisects ∠CAD

AE⊥ AF

∠CAF = ∠FAD (this is given)

∠BAE = ∠EAD (this is also given)

∠EAD + ∠FAD = 90° = ∠EAF (this is given too)

∠EAD + 1/2∠BAD and ∠FAD = 1/2 ∠CAD

1/2 ∠CAD + 1/2 ∠BAD= 90°

∠CAD + ∠BAD = 2x 90°

= 180°

The colinear point will lie on the straight line

and the straight line will make an angle of 180° on both sides.

∠CAD + ∠BAD

= ∠CAB = 180°

C,A, and B are colinear.

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