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:




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

michaelcai  Jul 25, 2017

1+0 Answers



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

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