# tangents.--missed this lesson

• Oct 22nd 2008, 07:58 AM
sallyishyper
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
• Oct 22nd 2008, 08:45 AM
Soroban
Hello, sallyishyper!

Quote:

\$\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 __ ?

• Oct 22nd 2008, 08:49 AM
masters
Quote:

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.