$AB$ is a chord of a circle, centre $O$, and $M$ is its midpoint . The radius from $O$ is drawn through the midpoint $M$. Prove that $OM$ is perpendicular to $AB$.
I know that the product of perpendicular lines is $(-1)$ but i dont know how to express this problem as a proof.
Best Answer
Lets focus on triangles MOA and MOB
OA = OB because O is center of circle and A and B are on the circle
AM = BM since M is midpoint of AB
Triangles MOA and MOB have MO in common
Therefore triangles MOA and MOB have same sides and same angles but are mirrored along OM.
This implies Angle OMA = Angle OMB .
Also these two angles are supplementary since OM falls on AB
Equal supplementary angles are right angles: Angles OMA and OMB are right angles