Let ABC be an equilateral triangle. Let P be any point on its incircle. Prove that:
AP2 + BP2 + CP2 = k for some constant k
Point P is in the interior of the equilateral triangle ABC. If AP = 7, BP = 5, and CP = 6, what is the area of ABC?
ABCD is a square and point P inside the square is such that PCD is an equilateral triangle. Find the angle α
Triangle ABC has a right angle at B. Let Q be along BC and P be along AB such that AQ bisects angle A and CP bisects angle C. If AQ = 9 and CP = 8√2, what is the length of the hypotenuse AC?
P is a point inside triangle ABC. Lines are drawn through P parallel to the sides of the triangle. The three resulting triangles with the vertices at P have areas 4, 9, 49 sq units. The area of triangle ABC is
