Shortest road? Geometry has a way!

How can we connect three towns with a junction so that the total road length is the shortest? The problem isn't as straightforward as it seems. Here'a a visual way to approach it.

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[GRIFFYBOIT]

When life gives you problems the answer is most probably a straight line

[Shinchan.badmass]

Yes but mitochondria is powerhouse of cell

[AshishRanjan-jnre]

This is fermat point of the triangle made from 3 vertex/towns.

[rutvikrs]

Kuch samajh me nahi aaya par sun ke bohot achha laga 😂

[vivek_kansal]

I thought it's the centroid of the triangle 😅

[PikaChuuuuuuuuuuuuuu]

Or just use the circumcenter of the triangle by drawing perpendicular to two of the sides

[modmateenkhan]

What's more basic is that you can take the common average of three points mak an arc and the all intersect is the shortest route

[gamechangerkl]

Shouldn't it be centroid of triangle

[devangghansyala]

Why we use this method, we simply find the centroid of triangle

[vasudevjs]

Is the point, centre of the incircle?🤔

[MatteoDolcin-yexm]

Poly bridge has taught me well, there have to be 3 120° angles between the lines

[Qder_XD]

isnt circumcentre an answer for shortest road?

[Geek]

In reality, the roads will be built between the towns forming a triangle because it’s easier to construct a straight line between two points than building a junction at all.

[YashKumar-uzuw]

What if we form a triangle out of these three dots...and then the centroid of the triangle may be the junction you are looking for...
Is it.... please tell me...

[Onnichan_in_pubg]

samajh me nai aaya, lekin sun ke accha laga

[rssl]

This is similar to a Soviet coffin problem where you had to rotate an equilateral triangle to get three angles in another triangle

[sunilyogita]

Are you that virat guy who usually comes in the show named gum hai kisi ke pyar me my mother use to watch that show

[aura_beast]

Hmmm but if we consider those three houses as vertex of triangle then from its incentre its distance will be the least right?(correct me with proof pls)

[princeray-isub]

Yes it's alright but i left with no pizza in my plate 😢

[arunmukta]

Name of the book where to find a proper explanation. This is not a proper explanation. What if there are n number of points.