In the figure below, AC = 20, BC = 5, and EC = 25. What is the length of DC?http://secure.starssuite.com/files/geo2010/geom_14S_Fig28.jpg

Question

anonymous · Answer

proportionally$$\frac{ 20 }{ 5 }=\frac{ 25 }{ DC }$$
$$DC=\frac{ 5*25 }{ 20 }=6.25$$

This is the approach I would take, however maybe someone else can confirm for me? @satellite73 ?

anonymous · Answer

this is a similar triangle problem

anonymous · Answer

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anonymous · Answer

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anonymous · Answer

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anonymous · Answer

bc is 25% of ac therefore cd must also be 25% of ec hence 25/4 = 6.25

ankit042 · Answer

From the circle we get products of the lengths of each secant segment and its external segment are equal.
AC*BC = EC*DC 
I am getting DC=4

ankit042 · Answer

@Mousam are you sure line BD will be parallel to AE?

anonymous · Answer

hm.... let me think.. also in the meantime... can you explain why AC*BC = EC*DC?? I've never come across that formula... sorry

ankit042 · Answer

check this out http://www.frapanthers.com/teachers/zab/Geometry(H)/GeometryinaNutshell/GeometryNutshell2005/Text/LengthsofSegments20052006.pdf page 3 has the proof you are looking for