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UV is tangent to W at point U.  What is the value of x?

 

 Mar 8, 2021
 #1
avatar+498 
-1

\((x - 1 + 2)^2 = (2x - 4)^2 + (x - 1)^2\)

 

\(x^2 + 2x + 1 = 4x^2 - 16x + 16 + x^2 - 2x + 1\)

 

\(2x = 4x^2 - 18x + 16\)

\(x = 2x^2 - 9x + 8\)

\(2x^2 - 10x + 8 = 0\)

\(2(x^2 - 5x + 4) = 0\)

2(x - 1)(x - 4) = 0

(x - 1)(x - 4) = 0

x = 4 

x = 1


However, side WU is (x - 1) so x can't be 1 since the side will be 0, which is impossible. 

Which means your answer is 4

 Mar 8, 2021
edited by Logarhythm  Mar 8, 2021

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