All perpendicular bisectors of a triangle concur at one point called circumcenter as a center of its circumscribing circle.

Bisectors of AB and BC meet at O. By ITT, we have , hence there’s a circle circumscribing

Corollary 1

All 3 bisectors of 3 sides of a triangle concur at ONE point called circumcenter.

There’s a unique line from O to mid-point of AC. By ITT, it must perpendicular to AC.

Corollary 2

The midpoint of hypotenuse of a right triangle is the center of its circumscribed circle

Draw a circle with diameter as one side of a triangle whose 3^rd virtex in on the circle. Now we need to prove it is a right triangle.

By ITT, we have

As sum of all angles in a triangle is 180⁰, so

Hence it is a right triangle.