Prove the following question : Bisectors of vertex angles A, B and C of a triangle ABC intersect its - Maths - Circles

Question

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
​

Ankita Agarwal · Accepted Answer

Dear Student,
<img alt="" height="288" src=
"https://s3mn%20mnimgs%20com/img/shared/discuss_editlive/4572370/2013_02_27_20_03_41/image6756765501358830201%20jpg"
width="310">
As we know in the given problem BD subtends angles ∠BED and
∠BAD
∠BED=∠BAD=∠A/2
AF subtends angles ∠ADF and ∠ACF
∠ ADF=∠ACF=∠C/2
∠ADE=∠ABE=∠B/2
Therefore, ∠ADE+∠ADF=∠C/2+∠B/2
⇒∠EDF=1/2(∠C+∠B)
=1/2(180-∠A) ( since ∠A+∠B+∠C=180º )
⇒∠EDF=90°–∠A/2

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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. ​

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.