**Proof: Suppose
ABC is a triangle with midpoints for its sides P,Q, and R.**

**Let l and m denote the
perpendicular lines at P and Q.
If l and m are parallel,
then AB and BC would also be parallel, but clearly , AB and BC are
not parallel lines, so l and m are not parallel.**

Then Tri (APO) is congruent to Tri(BPO) [SAS] and so

AO is congruent to BO. [CPCTC]

Similarly BO is congruent to CO.

so <ARO is congruent to <CRO... [CPCTC] .

**Note: **In
fact O is the center of the circle passing through the three vertices of
the triangle A,B, and C. O is the center of the circumscribed circle -
called the circumcenter- and the sides of the triangle are all chords of
this circle.