Orthogonality and Radical Axis of Circles An orthogonal line and a circle intersect at a single point called the center. The distance from the center to any...
Orthogonality and Radical Axis of Circles
An orthogonal line and a circle intersect at a single point called the center. The distance from the center to any point on the line is equal to the radius of the circle. The line and the circle are said to be orthogonal if they intersect at such a point.
The radical axis of a circle is the line that passes through the center of the circle and perpendicular to the radius vector. The radius vector is a vector from the center to any point on the circle.
A circle is completely determined by its radius, and its center is located at a fixed distance from the origin. The distance from the center to any point on the circle is equal to the radius.
Examples:
A line perpendicular to the radius of a circle through the center is also orthogonal to the circle.
A circle with a radius of 1 is orthogonal to all lines passing through its center.
Any line with a slope of -1 is perpendicular to the radius of a circle with a radius of 2