+0  
 
-1
38
1
avatar+1791 

Let P be a point in rectangle ABCD.  Compute PC.

 

 Aug 19, 2023
 #1
avatar+128731 
+1

Let D = (0, 0)

 

P =  ( 2,  6 - sqrt (4^2 - 2^2) )  = (2 , 6 - sqrt (12) )

C =  (4 ,0)

 

PC^2 =  (4 - 2)^2  + (6- sqrt (12))^2

 

PC^2 = 4 + 36 - 12sqrt (12) + 12

 

PC^2  = 52 - 12sqrt (12)

 

PC^2  = 52 - 24sqrt (3)  =   4 (13 - 6sqrt (3) )

 

PC = sqrt [ 4 ( 13 - 6sqrt (3) ) ] =  2 sqrt [ 13 - 6sqrt (3) ]  ≈  3.23

 

 

cool cool cool

 Aug 19, 2023

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