Geometry Stumper

[Albert Chan]

(08-15-2018 06:38 AM)Voldemar Wrote:  

(08-15-2018 12:39 AM)Albert Chan Wrote:  Angle(ACB) + 2 * Angle(ACD) = 180 degree (since it is just line extension)

How can You know that there are two equal angles (2*ACD). It must be proved.

Circle, with center D, inscribed the lines AB, AC, BC.
Connect D with those 3 touched line, so DF, DG, DH are radius of circle

What I "see" is triangle DCG, if flipped up, you get DCH.

Code:

           H 


D
                  C


           G

F      A                   B

Prove:
Right triangle DCG and DCH are congruent, since DC=DC (same line), DG=DH (both are radius).

-> Angle(DCG) = Angle(DCH)

Angle(ACB) + Angle(DCG) + Angle(DCH) = 180 degree

-> Angle(ACB) + 2 * Angle(ACD) = 180 degree