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

whats the radius?

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- June 2nd 2007, 02:03 PMstones44Circle 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

whats the radius? - June 2nd 2007, 02:40 PMCaptainBlack
- June 2nd 2007, 03:54 PMstones44
that doesnt really help

I need to find the radius - June 2nd 2007, 03:58 PMtopsquark
Pffl. It took me less than 30 seconds to google it. See here.

-Dan - June 2nd 2007, 04:01 PMJhevon
did you look up what the intersecting chord theorem was? see here

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

can you tell us what the solution is now? - June 3rd 2007, 12:50 AMCaptainBlack
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

follow this: link to Google.

**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 - June 3rd 2007, 06:36 AMstones44
its 15

sorry, just wasn't thinking - June 3rd 2007, 06:51 AMSoroban
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.

What is the radius?

Code:`C`

* * *

* |5 *

* 10 | 10 *

A*- - - - + - - - -*B

* |

* R * |R-5 *

* * *

* O *

* *

* *

* *

* * *

Let the radius be .

We have a right triangle with sides:

. .

- June 3rd 2007, 07:18 AMGAdams
- June 3rd 2007, 07:27 AMSoroban
Hello, GAdams!

Quote:

How did you get from: (r - 5)² to r² - 10r ?

*FOIL!*

. .

- June 3rd 2007, 07:55 AMGAdams
Thanks. I wasn't paying attention.

Excuuse: it's like Sunday today, right? - June 3rd 2007, 01:28 PMstones44
oooh thanks