Question

Prove that: If circle A = Circle B, CE = FH, DA = 2x+5, and GB = x +10, What is x?

Answer 1

By setting the segments DA and GB equal to each other due to the congruence of circle A and circle B, and solving the resulting linear equation, we find that the value of x is 5.

Step-by-step explanation:

To find the value of x, we first need to comprehend the relationship between the given circle properties and linear segments. As per the information, circle A is equal to circle B, implying that all corresponding segments and angles are congruent. The given lengths of DA and GB can be used as part of a system of linear equations since we have:

DA = 2x + 5

GB = x + 10

We are told that the circles are equal, so we can equate DA to GB:

(2x + 5) = (x + 10)

Now, let's solve for x:

1. Add -x to both sides of the equation to get rid of x on the right side:
   2x + 5 - x = x + 10 - x
   This simplifies to:
   x + 5 = 10
2. Subtract 5 from both sides of the equation to isolate x:
   x + 5 - 5 = 10 - 5
   This gives us:
   x = 5 Thus, the value of x is found to be 5.