Circle: Radius & Tangent
Radius Perpendicular to Tangent
One of the properties of circles is that at any given point P on the circle, the radius and the tangent passing through P are perpendicular to each other.
As such, in coordinate geometry, if the gradient of the radius is and the gradient of the tangent is , then
In specific cases,
- if the radius is horizontal, then its tangent will be vertical, and
- if the radius is vertical, then its tangent will be horizontal.
Check for Understanding 1
If the radius is vertical, then its respective tangent will be
Check for Understanding 2
If the radius is horizontal, then its respective tangent will be
Check for Understanding 3
It is given that C is the center of the circle, and P is a point on the circle. If the gradient of the tangent at P is 2, then the gradient of CP is