+0  
 
0
33
1
avatar

In triangle ABC, BAC = 78 degrees and ACB = 33 degrees. The incircle of triangle ABC touches sides BC, AC, and AB at D, E, and F, respectively. Find EFD in degrees.

 Jul 8, 2022
 #1
avatar+124525 
+1

                                    C

                                   33

                            E                  D

                                    O

       

    78     A                    F                        B 39

 

 

Let O be the center of the incircle

ECOD  forms a  quadrilateral  with angles  OEC and OED both being right

So  angle  EOD  =  180 - angle C  = 180- 33  = 147° =  minor arc ED

And angle EFD is an inscribed angle inrercepting this arc

So its measure = 147 /  2   =   73.5°

 

cool cool cool

 Jul 8, 2022

22 Online Users

avatar