Center of Triangle.

[Kieran]

A triangle has side lengths, y, y+ 16 and y + 44 cms. Find a point in the triangle equidistant from each side ? The formula for an incircle radius is 2a / p. Is there some similar formula for this problem ? Using Heron's formula is long , there must be a shorter way. Thank you. Do we bissect the sides ? Is this a midpoint , find where they meet ?

 

[DrPhil]

A triangle has side lengths, y, y+ 16 and y + 44 cms. Find a point in the triangle equidistant from each side ? The formula for an incircle radius is 2a / p. Is there some similar formula for this problem ? Using Heron's formula is long , there must be a shorter way. Thank you. Do we bissect the sides ? Is this a midpoint , find where they meet ?

The locus of all points equidistant from two of the sides is the bisector of the ANGLE between those two sides. If you find the point where two (or all three) of the angle bisectors intersect, that intersection will be equidistant from all three sides.