GEOMETRY HELP PLS

Question

Study the diagrem of cicle c, where two chords AB---- and DE-----, are equidistant from the center.

If AB= 3x-7 and DE= 5(x-5), what is the length of AB--------

Answer 1

If they are equal distance to the center, set them equal to each other to solve for x. Then, solve for the length of AB

3x-7=5(x-5) Distribute the 5

3x-7=5x-25 Subtract 3x from both sides

3x-7-3x=5x-25-3x Simplify

-7=2x-25 Add 25 to both sides

-7+25=2x-25+25 Simplify

18=2x Divide both sides by 2

18/2=2x/2 Simplify

9=x

AB=3x-7

AB=3(9)-7

AB=27-7

AB=20