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.[br][br]As such, in coordinate geometry, if the gradient of the radius is [math]m_r[/math] and the gradient of the tangent is [math]m_t[/math], then[br][center][math]m_r \times m_t = -1[/math][/center]In specific cases, [br][list][*]if the radius is horizontal, then its tangent will be vertical, and[/*][*]if the radius is vertical, then its tangent will be horizontal.[/*][/list]
If the radius is vertical, then its respective tangent will be
If the radius is horizontal, then its respective tangent will be
It is given that C is the center of the circle, and P is a point on the circle. [br]If the gradient of the tangent at P is 2, then the gradient of CP is