GH¯¯¯¯¯¯¯¯ is tangent to ⊙F at point G. What is the value of x?

Question

GH¯¯¯¯¯¯¯¯ is tangent to ⊙F at point G. What is the value of x?

1. A.
2. 2
3. 
   
4. B.
5. 3
6. 
   
7. C.
8. 4
9. 
   
10. D.
11. 5

Answer 1

Hey!

To begin, since I know GH is a tangent line, I can verify that segment FJ is also a radius of the circle! This means FJ also equals 2x - 1. We can now use the Pythagorean Theorem to find the value of x. **Keep in mind the hypotenuse will equal 2x -1 + 2 (segment JH) to equal 2x+1.

We have:

A = 2x+1.

B = x+2

C = 2x - 1

Set up the pythagorean theorem. You will have a few binomials to square but square everything and organize on one side first, and then begin to combine your like terms. You should get one root with a multiplicity of 2!

Hope this helps! Let me know if you need more assistance.