Given the right triangle:
ABC
Where angle B is the right angle.
Let's complete the given statement.
To find where the center of the circumscribed cirlce lies, let's first sketch the triangle and the circle.
A circumscribed circle is a circle which passes through all the vertices of a triangle.
By applying the converse of Thales theorem, we can see that the point D is center of the cirlce.
The point lies on line segment AC.
Also, the diameter of a circle is a line which passes through the center of the circle and touch the circumference at both ends.
Hence, line AC is the diameter of the circle.
Therefore, the complete statement is:
The center of the circumscribed circle of the triangle lies on segment segment AC, which is the diameter of the circle.
ANSWER:
The center of the circumscribed circle of the triangle lies on segment segment AC, which is the diameter of the circle.
