# Geometry problems!

• Apr 16th 2008, 06:39 AM
ncbabe
Geometry problems!
Okay so i got a giant packet full of everything and i don't get these 3 questions

There is a link attached to where the document is and it is on page 54 questions 4, 5 and 6

the archeology problem and thet pizza delivery problem.

http://mydragonnet.hkis.edu.hk/proce...25%2Fchp10.pdf
• Apr 16th 2008, 08:37 AM
Soroban
Hello, ncbabe!

Here's some help . . .

Code:

(4)                 C               * * *           *    3|    *       A* - - - * - - - *B       *  *    D|  12 *  *             *  |  *R       *      * | *      *       *        *        *                 O

We have: .$\displaystyle OA = OB = OC = R\text{ (radius)}$
. . . .and: .$\displaystyle AD = DB = 12$

Since $\displaystyle CD = 3$, then: .$\displaystyle DO = R-3$

In right triangle BDO, we have: .$\displaystyle (R-3)^2 + 12^2 \:=\:R^2$

. . which simplifies to: .$\displaystyle 6R \:=\:153 \quad\Rightarrow\quad\boxed{ R \:=\:\frac{51}{2}}$

Code:

(5)                   C               * * *           *      |  *         *        |    *       *          |      *                   |P     A* - - - - - o - - - *B       *  12.8    |  2.8  *       *          |      *                   |       *    22.4 |      *         *        |    *           *      |  *               * * *                   D
We're expected to know this theorem.

With two intersecting chords, the product of the segments of one chord
. . equals the product of the segments of the other chord.

In this problem: .$\displaystyle (CP)(PD) \:=\:(AP)(PB)$

So we have: .$\displaystyle (CP)(22.4) \:=\:(12.8)(2.8)\quad\Rightarrow\quad\boxed{CP \:=\:1.6}$