+256 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.
+37153 Circumference = 13 + 13 + 24 = 50 units
pi * d = circumferece
pi * d = 50
d = 50 / pi = 15.92 units
+129899 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
+37153 Good point, Chris! .... Wonder which one it is? Maybe yours because it didn't say ARC AB = ARC AC ? ~EP
