# Circle Question

• Jun 2nd 2007, 02:03 PM
stones44
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

• Jun 2nd 2007, 02:40 PM
CaptainBlack
Quote:

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
• Jun 2nd 2007, 03:54 PM
stones44
that doesnt really help

I need to find the radius
• Jun 2nd 2007, 03:58 PM
topsquark
Quote:

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
• Jun 2nd 2007, 04:01 PM
Jhevon
Quote:

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

Quote:

Originally Posted by stones44
that doesnt really help

I need to find the radius

can you tell us what the solution is now?
• Jun 3rd 2007, 12:50 AM
CaptainBlack
Quote:

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
• Jun 3rd 2007, 06:36 AM
stones44
its 15

sorry, just wasn't thinking
• Jun 3rd 2007, 06:51 AM
Soroban
Hello, stones44!

No fancy theorems needed . . .

Quote:

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.

Code:

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

Let the radius be $R$.

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

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

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

• Jun 3rd 2007, 07:18 AM
Quote:

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: $R-5,\:10,\: R$

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

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

How did you get from:
(r - 5)^2 to r^2 - 10r ?
• Jun 3rd 2007, 07:27 AM
Soroban

Quote:

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

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

• Jun 3rd 2007, 07:55 AM
Thanks. I wasn't paying attention.

Excuuse: it's like Sunday today, right?
• Jun 3rd 2007, 01:28 PM
stones44
oooh thanks