1. ## tangents.urgent!!!!!!!!

O is the centre of a circle. P is a point on its circumference. the gradiant of OP is 2. what is the gradient of tangent P.

can i also please have an explanation

2. Hello, sallyishyper!

$\displaystyle O$ is the centre of a circle. $\displaystyle P$ is a point on its circumference.
The gradient of $\displaystyle OP$ is 2.
What is the gradient of the tangent at $\displaystyle P.$

We are expected to know this theorem:
The tangent to a circle is perpendicular to the radius to the point of tangency.

If the gradient of the radius is 2, then the gradient of the tangent is __ ?

3. Originally Posted by sallyishyper
O is the centre of a circle. P is a point on its circumference. the gradiant of OP is 2. what is the gradient of tangent P
A radius (OP) is perpendicular to the tangent line at the point of tangency (P). The slope (gradient) of perpendiculars are negative reciprocals of each other. Since the radius has gradient = 2, the gradient of the tangent line is -1/2.