Question

What is the value of x if A E equals x plus 2 mm, E B equals 8 mm, C E equals 3 x mm, and E D equals 4 mm? Circle with center Q has points A, D, B and C on the perimeter. Line segment C D crosses line segment A B at point E.

Answer 1

x = 4

Explanation:

The product of the lengths of the segments of each chord is the same.

AE·EB = CE·ED

(x+2)(8) = (3x)(4) . . . . . substitute the given lengths

8x +16 = 12x . . . . . . . . simplify

16 = 4x . . . . . . . . . . . . . subtract 8x

4 = x . . . . . . . . . . . . . . . divide by 4