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In triangle ABC, BAC = 78 degrees. The incircle of triangle ABC touches sides BC, AC, and AB at D, E, and F, respectively. Find EDF in degrees.

 

 Mar 22, 2021
 #1
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Let the centor of  the incircle  =  O

 

Then  angles  AEO  and  AFO  = 90°

 

And in quadrilateral AFOE....angle  FOE  can be found as

 

90 + 90 +78  + angle FOE  =  360

 

258  + angle FOE  =  360

 

angle FOE =  360 - 258   =   102° 

 

And angle EDF is an inscribed  angle in the  incircle that  subtends  the  same arc as angle FOE

 

So...angle  EDF  = (1/2) 102  =  51°

 

 

cool cool cool

 Mar 22, 2021

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