In triangleABC

D is a point on BA such that BD:DA = 1:2

E is a point on CB such that CE:EB = 1:4

DC and AE intersect at F

I am suppose to find CF:FD(express the ratio in terms of two positive whole numbers) Help!

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- February 8th 2009, 05:27 PMkgk[SOLVED] Geometry
In triangleABC

D is a point on BA such that BD:DA = 1:2

E is a point on CB such that CE:EB = 1:4

DC and AE intersect at F

I am suppose to find CF:FD(express the ratio in terms of two positive whole numbers) Help! - February 9th 2009, 02:27 AMGrandadGeometry
Hello kgkYou can solve this using ratios and position vectors. See my post at http://www.mathhelpforum.com/math-he...tml#post262231 for the basic formula.

In your problem, if we denote the position vectors of A, B, ... by then

If we suppose that F divides CD in the ratio 1:n, and EA in the ratio 1:m, then have two ways of expressing .

Using CF:CD = 1:n,

Using EF:FA = 1:m,

If we equate these two expressions for and compare coefficients of , and , we get:

(1)

(2)

(3)

From (2) and (3):

Check: . Subst into (1):

So the ratio CF:FD = = 3:8.

Grandad