The center of the circumscribed circle lies on line segment and the longest side of the triangle is equal to the of the circle.

Answer with explanation:

It is given that point , O is the center of circle passing through points A, B, and C.

Also, ΔABC is a Right Angled Triangle.

→→When, you draw Perpendicular Bisectors of  Sides AB , BC and AC of Right Triangle ABC, it will meet at the mid point of side AC, which is the center of circle having center O. This is called Circumcenter.

Why Perpendicular bisector,because Perpendicular from center to the chord bisects the chord.AB, BC and AC are the chords of the circle.

→→ The center of the circumscribed circle lies on line segment ,AC and the longest side of the triangle is equal to Hypotenuse, which is Diameter of the of the circle.

Solution:

Given : Point O is the center of a circle passing through points A, B, and C as well as Triangle ABC is a right angled triangle.

Solution:

Keep in Mind

1. If a circle passes through all  three vertices of triangle , that circle is called Circumcircle and it's center lies on the intersection of perpendicular bisector of three sides.In a right angled triangle  perpendicular bisector lies on mid point of Hypotenuse.

As given ABC is right angled triangle, so

Perpendicular bisector will lie on the mid point of Hypotenuse,which is center of circle and and the longest side of the triangle is equal to hypotenuse, which is Diameter of the Circle.