Question 46
We are given a triangle $ABC$ and a point $P$ in its interior. The lines through $P$ and parallel to the sides of the triangle divide the triangle into three parallelograms and three triangles.
a) If $P$ is the incenter of $ABC$, show that the perimeter of each of the three small triangles is equal to the length of the adjacent side.
b) For a given triangle $ABC$, determine all inner points $P$, such that the perimeter of each of the three small triangles equals the length of the adjacent side.
c) For which inner point does the sum of the areas of the three small triangles attain a minimum?
a) If $P$ is the incenter of $ABC$, show that the perimeter of each of the three small triangles is equal to the length of the adjacent side.
b) For a given triangle $ABC$, determine all inner points $P$, such that the perimeter of each of the three small triangles equals the length of the adjacent side.
c) For which inner point does the sum of the areas of the three small triangles attain a minimum?