Point P is selected uniformly at random in the interior of square ABCD. What is the probability that angle APD is obtuse (greater than 90 degrees)?

ABCD is a square and point P inside the square is such that PCD is an equilateral triangle. Find the angle α

Suppose ABCD is a square. Let E be interior to the square such that EDC = ECD = 15°. What is the measure of angle EBC?

In trapezoid ABCD, the sides AB and CD are parallel and AB > CD. Point P is in the interior, dividing the trapezoid into 4 triangles with areas CPD = 2, CPB = 3, BPA = 4, APD = 5. What is AB/CD equal to?

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?