If `a=9,b=4a n dc=8` then find the distance between the middle point of BC and the foot of the perpendicular form `Adot`

Explanation

We can create a triangle `ABC` with the given details.

Please refer to video to see the diagram.

We have to find `DE`.

From the diagram,

`DE = CD - CE = a/2- bcosC`

`=>DE = a/2 - b((a^2+b^2-c^2)/(2ab))`

`=(a^2-a^2-b^2+c^2)/(2a)`

`=(-b^2+c^2)/(2a) = (-(4)^2 +(8)^2)/(2(9))`
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