What is a normal in circle geometry???

Probably a realllyy stupid question but I missed the lessons at school about circle geometry, and now I'm revising and actually have no clue what a normal is??

Theres no good notes in my revision book either so does anybody know of any good websites that we will explain circle geometry - normals, tangents etc... because I'm very confused!!

I know how to calculate midpoints, and radius, just not normals!!

If somebody could explain to me about normals I'd much appreciate it!!

Reply 1

uer23

A tangent to a circle is a line which touches the circle at one point only.

A normal is perpendicular to the tangent.

Reply 2

*MJ*

Nothing is normal in Mathematics...

Which is why it is so brilliant. :king1:

Anyway, it terms of circles, it is the line perpendicular to the tangent (where the line meets the curve or circle at one point) and the products of their gradients is equal to minus 1.

E.g. when gradient of tangent is represeted by m1 and gradient of normal is represented by m2...

m1 x m2 = -1.

This is very useful as sometimes you would have the gradient of the tangent and be asked to find the equation of the normal using the co-ordinates (x,y). In order to do this, you must first find the gradient of the normal i.e. m2 = -1 / m1 and then put it into the formula y - y1 = m(x - x1).

Also in circle geometry, the general equation is (x-a)^2 + (y-b)^2 = r^2 where r denotes the radius of a circle and a and b the centre. This is obtained by completing the square and taking all constant terms to the right hand side (r^2 side).

Good luck OP and post if you have any further problems. :smile: