# Tangent to the centrum edge of a circle

• mimi.janson
In summary, the conversation discusses finding the point of intersection between a given line and circle, in order to prove that the line is a tangent to the circle. The formula for finding the distance between a line and a point is mentioned, but the correct point to plug in is debated. It is eventually determined that the centre of the circle should be used, but the calculated result does not match the known centre of the circle. Further discussion and steps are needed to find the correct solution.
mimi.janson

## Homework Statement

Hi i have a circle that is shown by (x-7)2+(y+1)2=20

i also have a line y=2x-5 and i have to explain why the line is a tangent to the edge of the circle

i know that the circle has the centre in (7,1) and that the radius of it is 4,4

## Homework Equations

i know i have to use the formula G =l ad+be+c l/√a2+b2

where the result should be something like the centre +4,4

## The Attempt at a Solution

i have tried to change my y=2x-5 so it stands in the form ax+by+c=0 and i think it will end up like 2x+1y+(-5)=0 but i really don't know what to do next. I have attached a photo of what i mean with the tangent. the one that i am speaking about is the red

#### Attachments

• CIRCLE_LINES_svg.png
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mimi.janson said:
i know i have to use the formula G =l ad+be+c l/√a2+b2
You don't have to. And if you want to use it, you should find out what it does, and what a,b,c,d and e are.

y=2x-5 is not the same as 2x+1y+(-5)=0, there is a sign error.

Do you know how to compute the distance between a line and a point?

mimi.janson said:
i know i have to use the formula G =l ad+be+c l/√a2+b2
That's the distance from the line ax+by+c=0 to the point (d,e), right?
What point do you think you should plug in?
i have tried to change my y=2x-5 so it stands in the form ax+by+c=0 and i think it will end up like 2x+1y+(-5)=0
Not quite. You have a sign wrong.

haruspex said:
That's the distance from the line ax+by+c=0 to the point (d,e), right?
What point do you think you should plug in?

Not quite. You have a sign wrong.

sorry i am not sure if i understand what you mean with what point i should plug in

if you mean what i think i should write in the formula then i believe it is G =l -2*7+0*1+5 l/√a-2+02

but that just comes out wrong for a reason.

with asking if i know how to compute the answer if it means if i know how to use a computer to solve it i already tried. My problem is that the computer shows me that the centre of the circle is in 7,-1 instead which i don't understand

I'm not familiar with your G formula. Are you required to use it?

If not, you could approach the problem by trying to find where the line intersects the circle. There are three possibilities: (1) the line intersects the circle in two distinct points (2) the line intersects the circle at only one point (3) the line doesn't intersect the circle at all.

TSny said:
I'm not familiar with your G formula. Are you required to use it?

If not, you could approach the problem by trying to find where the line intersects the circle. There are three possibilities: (1) the line intersects the circle in two distinct points (2) the line intersects the circle at only one point (3) the line doesn't intersect the circle at all.

but that is also what the formula i had shows.

it shows you the distance between the centre of the circle and the line. Then you will know if that distance is bigger than the radius it doesn't intersect the circle if its smaller than the radius it means it does intersect it two times and if it is the same then that would be one time and also the right answer

how do you do it?

mimi.janson said:
but that is also what the formula i had shows.

it shows you the distance between the centre of the circle and the line. Then you will know if that distance is bigger than the radius it doesn't intersect the circle if its smaller than the radius it means it does intersect it two times and if it is the same then that would be one time and also the right answer

how do you do it?

OK. I didn't know what the symbols in your G equation stood for. Ignore my post and carry on!

mimi.janson said:
how do you do it?

To find where the line intersects the circle, you solve the circle and line equations simultaneously. The line equation says y = 2x-5. You could substitute this expression for y into the circle equation and try to solve the resulting equation for x.

TSny said:
To find where the line intersects the circle, you solve the circle and line equations simultaneously. The line equation says y = 2x-5. You could substitute this expression for y into the circle equation and try to solve the resulting equation for x.

so you mean i just have to isolate x in the circle by putting 2x-5 in the place of y and then find x?

i just did and it says 5 over 2.6 ...thats not right it should be 4,4

mimi.janson said:
so you mean i just have to isolate x in the circle by putting 2x-5 in the place of y and then find x?
Yes, that's how you do it.
i just did and it says 5 over 2.6 ...thats not right it should be 4,4

You wouldn't expect x to be 4.4. But it's not 5/2.6 either. If you post your steps we can look at it.

The center of the circle is not at (7,1) according to the equation you have given in the OP.

mimi.janson said:
sorry i am not sure if i understand what you mean with what point i should plug in
The formula you quote is for the distance from a line to a point. You are trying to show that this line is a tangent to a circle of known centre and radius. So for what point would it be useful to know its distance from the line?
if you mean what i think i should write in the formula then i believe it is G =l -2*7+0*1+5 l/√a-2+02
Looks like you tried plugging in the correct point (the centre of the circle) but I can't tell whether you did it correctly because I cannot tell what signs you used. Also, as I mentioned, you had a sign wrong in converting the eqn to ax+by+c=0. So to make sure we have things right, please list what values you are filling in for a, b, c, d and e. (The '0' you have in the formula for G is definitely wrong. None of them are 0.)

## 1. What is the definition of a tangent to the centrum edge of a circle?

A tangent to the centrum edge of a circle is a line that touches the circle at exactly one point, called the point of tangency. This line is perpendicular to the radius of the circle at the point of tangency.

## 2. How is the point of tangency determined on a circle?

The point of tangency is determined by drawing a line from the center of the circle to the point where the tangent line touches the circle. This line is perpendicular to the tangent line and is called the radius of the circle at the point of tangency.

## 3. What is the relationship between a tangent line and a radius of a circle?

A tangent line and a radius of a circle are always perpendicular to each other at the point of tangency. This means that they form a 90 degree angle and are not intersecting.

## 4. How many tangents can be drawn to a circle from a given external point?

There can be two tangents drawn to a circle from a given external point. These tangents will be equal in length and form a 90 degree angle with the radius at the point of tangency.

## 5. What is the significance of tangents to the centrum edge of a circle in real life?

Tangents to the centrum edge of a circle have many real-life applications, such as in optics, where they are used to determine the angle of incidence and angle of reflection of light rays on curved surfaces. They are also used in navigation and engineering to determine the best path for a moving object to take around a curved obstacle.

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