+0

# Geometry Problem

0
73
3

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

### 3+0 Answers

#1
+2

Circumference = 13 + 13 + 24 = 50  units

pi * d = circumferece

pi * d = 50

d = 50 / pi = 15.92 units

Feb 22, 2021
#2
+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   Feb 22, 2021
#3
+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