Question

Study the diagram of circle 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

20 units

Explanation:

Chords the same distance from the center have the same length, so ...

AB = DE

3x -7 = 5(x -5)

3x -7 = 5x -25 . . . . . eliminate parentheses

18 = 2x . . . . . . . . . . . add 25-3x

9 = x . . . . . . . . . . . . . divide by 2

AB = 3x -7 = 3(9) -7 = 20

The length of AB is 20 units.