Here is a geometric method that enables you to find the center of a circle.

The principle rests on the following property: a right triangle inscribed in a circle has for its hypotenuse the diameter of the circle.

The incenter of a triangle is the point of intersection of the triangle's three angle bisectors.

Move the point C around the circumcircle to prove that the triangle remains always right.

The sum of interior angles in any triangle is 180 degrees (PI radians). You can click and drag the vertices or the sides of the triangle.

Here you have one of the numerous geometric demonstrations of the Pythagorean Theorem.

The orthocentre H is the intersection of the three heights of a triangle. You can modify the shape of the triangle.

Notice that each of the 4 points A,B,C,H of the figure is the orthocenter of the triangle made with the three others.

The centroid of a triangle is the point where the three medians meet. This point is also called the center of mass for the triangle. You can modify the shape of the triangle.

The perpendicular bisectors of the sides of a triangle meet in a common intersection point. This point is the center of the circumscribed circle, or circumcenter. The animation illustrates the use of a compass in geometric constructions.