But I thought angles in the same segment are all equal. Even though we move the point N, the magnitude of the angles are still the same
Let AB be a chord in a circle, and M is a point on the circle in the major segment.
If CD is another chord in the same circle such that length of CD= length of AB, and N is another point on the circle in the major segment(corresponding to chord CD).
Is Angle AMB = Angle CND??
Seems like they are the same, is there a proof for this?
There is a rule/theorem/conjecture/?/wahtever in Geometry that says an inscribed angle in a circle is half the measure of the arc subtended by the angle.
And, there should be a rule/theorem/?/whatever in Geomerty also that says, in effect, that chords of the same lenght substend circular arcs/circular segments that are the same in length also.
If there is none, then it is easy to prove that, anyway. Chords of same lengths have equal central angles, blah, blah.
Play with those and you will find that, indeed, angle AMB = angle CND.