Prove the following question :

Bisectors of vertex angles A, B and C of a triangle ABC intersect its circumcircle at the points D, E and F respectively. Prove that angle EDF = 90​o - 1/2 angle A.

Dear Student,

As we know in the given problem BD subtends angles ∠BED and ∠BAD


AF subtends angles ∠ADF and ∠ACF

∠ ADF=∠ACF=∠C/2


Therefore, ∠ADE+∠ADF=∠C/2+∠B/2


 =1/2(180-∠A)                 ( since ∠A+∠B+∠C=180º )


Hope this information will clear your doubts about topic.

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