Analytical Geometry
how to find incentre of triangle when three vertices are given
how to find incentre of triangle when three vertices are given
2 Answers
Dear student,
The significance of the incentre is a point where the radius must be drawn from to have the biggest possible circle which touches all of the sides of the triangle.
The incentre always remains inside the triangle as the name suggests because the circle it is the centre of must be located inside the triangle
After we tested the four different triangles (2 by computer 2 by hand) the significance of the incentre we stated at the beginning was correct; the incentre is a point which always remains within the triangle and is the point where the radius must be drawn from to have the biggest possible circle which touches all of the sides of the triangle.
Let the triangle be ABC in which vertices are A(x1,y1), B(x2,y2) and C(x3,y3).
`Let AB= a.
BC= b.
AC= c.
Then
Incenter(x,y) = ( ax1+bx2+cx3)/(a+b+c) , (ay1+by2+cy3)/(a+b+c)).
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