1. Let triangle ABC be a equilateral triangle with length equals to 1. Let point P be an arbitrary point in the interior of triangle ABC, D be point on BC, E be point on CA, and F be point on A, so that PD∥AB, PE∥BC, and PF∥AC. Find the value of PD+PE+PF.
2. In equiangular octagon ABCDEFGH, AB=CD=EF=GH and BC=DE=FG=HA. Argue that AB⊥CD.
For 1, join P to A, B and C forming three triangles. Calculate the area of each and say that their sum is equal to the area of ABC.
The area of APC, for example, will be its base, AC (=1) multiplied by its height (= PE.cos30) divided by 2, etc. .
The wording for 2 seems a bit loose, what, exactly, is meant by equiangular ?
Which angles are equal ?
If its just the angles between successive sides, then its obvious.