Q. 84.0( 46 Votes )
Bisectors of angles A, B, and C of a triangle ABC intersect its circumcircle at D, E and F respectively. Prove that the angles of the triangle DEF are 
and 
Answer :
It is given in the question that,
∠ABE = 
However,
= ∠ADE
Like this, similarly
∠ACF = ∠ADF = 
D = ∠ADE + ∠ADF
= 
+ 
= 
(∠B + ∠C)
= 
(180o – ∠A)
= 90o - 
∠A
Similarly,
E = 90o - 
∠B
And,
F = 90o - 
∠C
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