The bisectors AD and CE are drawn in the triangle ABC. Find the length of the segment DE. If AC = 6, AE = 2, CD = 3.

To solve, we need to make an equation, then let EB = x; BD = y;
It turns out that we can make up the proportion:
BD / AB = DC / AC;
The proportion looks like this because the bisector divides the opposite side into segments proportional to the adjacent sides of the triangle.)
Let’s find:
y / (2 + x) = 3/6;
x / (y + 3) = 2/6;
Thus:
x = 8/5;
y = 9/5
We also note that ∠B = 90 ° (since AB² + BC² = AC² by the Pythagorean theorem);
Find ED:
ED = √ (x² + y²);
ED = (√145) / 5;
Answer: ED = (√145) / 5;



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