We need to find the distance from point of intersection of the 2 legs of the triangle to the point of intersection of the Angular bisectors.
The Point where the angular bisectors intersect is called "Incentre".
Denoted by "I".
Draw a line from the Incentre to the side of length 2 units.
This Line divides that side BC into two parts.
Let denote those parts by x and y.
This line makes two triangles, such that
one triangle is 30 - 60 - 90 triangle and the other one is 45-45 -90 triangle.
Let x be the length of the part in the 45-45-90 triangle and
y be the length of the part in the 30-60-90 triangle.
So,
The side opposite to is times the side opposite ,
Plug in the
So, the Hypotenuse in the triangle 45-45-90 is times the length of a leg.
So, the Hypotenuse is
Answer:
The distance from the point of intersection of the legs to Incentre is .
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