If D is the mid-point of CA in triangle ABC and is the area of triangle,then show that
where a=BC,b=CA and c=AB
Hello,
Please have a look at the sketch.
BE is the altitude of the triangle coming from B.
Thus
Note that you want . Obviously, it is equal to because the triangle BED is a right angle triangle in E.
Now, you'll have to calculate ED, since you already know the others.
D is the midpoint of AC. Therefore
And
If we multiply by 2, we can write
Applying Pythagoras theorem in AEB, we have
Applying Pythagoras theorem in BEC, we have
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See the two boxed formula ?
This gives :
Multiply by
And please observe
(in fact, the important step was to multiply the denominator by its conjugate, and it just popped up that it was the length b)
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There may be a shorter way, but I don't know... Inspire yourself from it