Bisectors of angles A, B and C of a triangle ABC intersect its circum circle at D, E and F respectively. Prove that the angles of the triangle DEF are and

Bisectors of angles A, B and C of a triangle ABC intersect its circum circle at D, E and F respectively. Prove that the angles of the triangle DEF are and

It is given in the question that,

∠ABE =

However,

= ∠ADE

Like this, similarly

∠ACF = ∠ADF =

D = ∠ADE + ∠ADF

= +

= (∠B + ∠C)

= (180^o – ∠A)

= 90^o - ∠A

Similarly,

E = 90^o - ∠B

And,

F = 90^o - ∠C

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