# Math Help - Circle Question

1. ## Circle Question

You have a circle....a chord AB is 20 inches long....the distance between the midpoint of AB and the nearest point on the circle is 5

2. Originally Posted by stones44
You have a circle....a chord AB is 20 inches long....the distance between the midpoint of AB and the nearest point on the circle is 5

You need the intersecting chord theorem (and a diagram).

RonL

3. that doesnt really help

I need to find the radius

4. Originally Posted by stones44
that doesnt really help

I need to find the radius
Pffl. It took me less than 30 seconds to google it. See here.

-Dan

5. Originally Posted by stones44
that doesnt really help

I need to find the radius
did you look up what the intersecting chord theorem was? see here

EDIT: Dan's site seems a lot nicer than mine

Originally Posted by stones44
that doesnt really help

I need to find the radius
can you tell us what the solution is now?

6. Originally Posted by stones44
that doesnt really help

I need to find the radius
No you need to learn how to do research for yourself, you have been given
the name or the result you need. Now it seems improbable that you have not
covered this in class, so it will be in your notes or text book.

Now where I come from text books have indexes, so you could try looking it
up in the index. Also you could, as you appear to have access to the
internet, try typing it into Google. If you don't know what Google is then

Intersecting Chord Theorem

Let AB and CD be two chords in the same circle that intersect at a point
X. Then:

|AX|*|XB| = |CX|*|XD| ... (1)

(Where |UV| denotes the length of the line segment UV.)

Now look at the diagram I posted. Do you see two intersecting chords?
Have I marked their lengths?

So now label the points as in the statement of the theorem and then
note which lengths appear in the statement of the intersecting chord
theorem and so write (1) in terms of the lengths of these chords.

Now solve the resulting equation for R.

RonL

7. its 15

sorry, just wasn't thinking

8. Hello, stones44!

No fancy theorems needed . . .

You have a circle and a chord AB is 20 inches long.
The distance between the midpoint of AB and the nearest point on the circle is 5.
What is the radius?
Code:
                C
* * *
*     |5    *
*  10   |   10  *
A*- - - - + - - - -*B
*     |
*    R *  |R-5      *
*         *         *
*         O         *

*                 *
*               *
*           *
* * *

Let the radius be $R$.

We have a right triangle with sides: $R-5,\:10,\: R$

$R^2\:=\:(R-5)^2+10^2\quad\Rightarrow\quad R^2 \:=\:R^2 - 10R + 25 + 100$

. . $10R \:=\:125\quad\Rightarrow\quad R\:=\:12.5$

9. Originally Posted by Soroban
Hello, stones44!

No fancy theorems needed . . .

Code:
                C
* * *
*     |5    *
*  10   |   10  *
A*- - - - + - - - -*B
*     |
*    R *  |R-5      *
*         *         *
*         O         *

*                 *
*               *
*           *
* * *

Let the radius be $R$.

We have a right triangle with sides: $R-5,\:10,\: R$

$R^2\:=\R-5)^2+10^2\quad\Rightarrow\quad R^2 \:=\:R^2 - 10R + 25 + 100" alt="R^2\:=\R-5)^2+10^2\quad\Rightarrow\quad R^2 \:=\:R^2 - 10R + 25 + 100" />

. . $10R \:=\:125\quad\Rightarrow\quad R\:=\:12.5$

How did you get from:
(r - 5)^2 to r^2 - 10r ?

How did you get from: (r - 5)² to r² - 10r ?
Have you forgotten your basic algebra? . . . FOIL!

. . $(R - 5)^2 \;=\;(R-5)(R-5)\;=\;R^2 - 5R - 5R + 25 \;=\;R^2 - 10R + 25$

11. Thanks. I wasn't paying attention.

Excuuse: it's like Sunday today, right?

12. oooh thanks