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# Bisectors

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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.

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
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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°

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

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