What's so special about that point?
Geometry
Level
pending
A point lies inside a triangle with sides 5, 12 and 13 such that it is equidistant from the sides of the triangle. Find that distance.
The answer is 2.
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1 solution
The point which is equidistant from the sides of a triangle is its INCENTRE (the centre of the inscribed circle) !!!
So for calculating the distance from the side we just need to find
the inradius of the triangle , which is given by the formula→
▲ = rs , where
r = inradius ,
s = semi perimeter &
▲ = area of triangle
Now we find that its a right triangle ,
Hence ▲ = (1/2)•(5)•(12) = 30 &
s = ( 12 + 5 + 13)/2 = 15
Putting these values in ▲ = rs
We get , r = 2 .....! THANK YOU ★