文[1]指出:若△ABC的面积为△,勃罗卡角为α,则以勃罗卡点在三边的射影为顶点的三角形的面积为△sin2α.笔者发现,在双圆四边形中也有定理设P是双圆四边形ABCD的勃罗卡点,∠PAB=∠PBC=∠PCD=∠PDA=α,P点在AB、BC、CD、DA上的射影分别为A′、B′、C′、D′.记四边形ABCD的面积 The article [1] pointed out that if the area of ​​△ABC is △ and the angle of Broca is α, then the area of ​​the triangle with the Brocade point on the three sides of the vertexes is △sin2α. The author found that in the double-circle quadrilateral There is also a theorem that P is the Broca point of the double-circle quadratic ABCD, ∠PAB=∠PBC=∠PCD=∠PDA=α, and the projections of point P on AB, BC, CD, DA are A′, B′, respectively. C’, D’. Record the area of ​​quadrilateral ABCD.