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An archaeologist finds a piece of an ancient wheel. In order to find the diameter of the wheel,

she marks three points A, B and C on the arc of the wheel so that AB = AC.  If AB = 13 and BC = 24,

find the diameter of the wheel.

 Feb 21, 2021
 #1
avatar+31281 
+2

Circumference = 13 + 13 + 24 = 50  units

 

pi * d = circumferece

pi * d = 50

d = 50 / pi = 15.92 units

 Feb 22, 2021
 #2
avatar+118069 
+1

I interpreted  this one a little differently  than EP  did

I saw  AB , AC  and BC  as  being  chord lengths

 

Thus  we  have  triangle ABC with  sides of 13, 13  and  24  and  the  wheel  is  the  circumcircle of this triangle

 

The  circumradius   = 

 

                             13 * 13  * 24

____________________________________________________   =

sqrt [( 13 + 13 + 24) (13 + 13  -24) ( 24 + 13 - 13) (24 + 13 - 13) ] 

 

 

                              4056

 __________________________________   = 

         sqrt [ 50  * 2 * 24 * 24  ] 

 

                             4056

             ________________  =

                sqrt  [ 57600 ]  

 

                          4056

                      _______  = 

                          240

 

                             16. 9

 

So.....the diameter   =    2 * 16.9  =     33.8  in

 

 

cool cool cool

 Feb 22, 2021
 #3
avatar+31281 
+1

Good point, Chris! ....   Wonder which one it is?   Maybe yours because it didn't say ARC AB = ARC AC  ?    ~EP

ElectricPavlov  Feb 22, 2021

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