Question

find the actual lengths

Answer 1

Hello Friend ! 

Here's is the answer to your query !

Hope it helps :-
 
Since the point of intersection of tangent and radius makes $90^{0}$ angle .

Therefore by using pythagorus theorem :

(x-1)²  + (x+3)² = (x+1)²

⇒ (x²  - 2x + 1) + (x² + 6x + 9) = x² + 2x + 1

⇒ 2x² + 4x + 10 = x² + 2x + 1 

⇒ x² + 2x + 9 = 0 

⇒ x² + 2x + 1 - 1 + 9 = 0

⇒ (x + 1)² =  -8 

⇒ (x + 1) = 2√2

⇒ x = 2√2 - 1

This is your answer.

Hope this cleared your doubt !
 

Answer 2

Answer:

I have attached above the solution

give thanks if it helped

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