In the diagram, AE¯¯¯¯¯¯¯¯ is tangent to the circle at point A, and secant DE¯¯¯¯¯¯¯¯ intersects the circle at points C and D. The lines intersect outside the circle at point E.

Question

A circle with no center shown. Points A, C, and D lie on the circle. Tangent A E and secant D E are as described in the text. Segment A E equals 12, segment E C equals 8, and segment C D equals x plus 10.

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What is the length of ED¯¯¯¯¯¯¯¯?
21
23
20
18
could somebody help im really stuck on this one

Answer 1

So am I. What is x about?

Answer 2

Recall the secant-tangent theorem, and you have
EA^2 = EC*CD
12^2 = 8*(x+10)
and now ED = EC+CD = 8+x+10

I suspect a typo somewhere in the murk above

Answer 3

18