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?
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°