In square ABCD, e is the midpoint of CD, P is ad, and angle APB = angle BPE. Then the value of Tan angle APB is

In square ABCD, e is the midpoint of CD, P is ad, and angle APB = angle BPE. Then the value of Tan angle APB is

As shown in the figure, it is easy to prove that the triangle ABP is equal to the triangle EBP. So be = ab. because e is the midpoint of CD, be = 2ec. In the right triangle BEC, be = 2ec, so the angle EBC = 30 degrees. So the angle dep = 30 degrees, and the angle DPE = 60 degrees

1. In the square ABCD, e is an internal point and the triangle BCE is an equilateral triangle
2. In square ABCD, e is the midpoint of BC, CF = quarter of CD, if AB = 4, calculate the area of triangle AEF

1.
75 degrees
Because AB = BC = be
So the triangle Bae is an isosceles triangle
And the angle Abe = 30 degrees
So BAE = (180-30) / 2 = 75 degrees
two
five
From Pythagorean theorem, we can get AE = 2 times root 5, EF = root 5, AF = 5
And the three sides just form a right triangle
So area = (AE * EF) / 2 = 5