Question

The ray of the light from point M, reflected from the line AB at point C, then goes through point N. Prove that the bisector of the angle MCN is perpendicular to line AB

Answer 1

see the prove below

Explanation:

Let bisector of angle MCN is KC. Points N,M,K are on the one side from the line AB

Let MCB=x. So the NCA is x as well ( the angle of ray reflection NVA is equal to the angle of ray putting on the line MVB).

The value of angle ACB=180 degrees, because AB is a straight line.

KC is MCN bisector, so KCN=KCM =y.

So ACB= KCN+KCM+MCB+NCA=x+x+y+y=2x+2y=180

=> x+y=90 degrees => KC is perpendiculat to line AB.

The statement is proved