+0  
 
0
61
1
avatar+63 

In triangle $ABC$, \(\angle BAC = 72^\circ\). The incircle of triangle $ABC$ touches sides $BC$, $AC$, and $AB$ at $D$, $E$, and $F$, respectively. Find $\angle EDF$, in degrees.

 

Link to diagram:

 

https://latex.artofproblemsolving.com/0/0/a/00af01b8929e78fd074011c2a75baf7d2f45f0a6.png

 

can anyone tell me how to put a diagram onto web2.0calc.com?

michaelcai  Jul 25, 2017
Sort: 

1+0 Answers

 #1
avatar+75352 
+2

 

Note that if we called the center of the circle, O, then radii drawn to both tangent points F and and E would form right angles AEO and  AFO......so.....FAEO  would form a quadrilateral such that  angle FOE would be suppllemental to angle  FAE  = angle BAC .

 

So....angle FOE  = 180 - 72 =  108°

 

And since FOE is a central angle intercepting the same arc as the inscribed angle FDE, then  FDE  = (1/2) FOE  = (1/2) 108  =  54°

 

 

cool cool cool

CPhill  Jul 25, 2017
edited by CPhill  Jul 25, 2017

17 Online Users

avatar
avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details