 Hi, and how are you all today? I am Priyanka. The question says, diagonal AC and VD of a coordinate of A, B, C, D intersect each other at P. Show that area of A, P, B into area of C, P, D is equal to area of A, P, D into area of B, P, C. Now let's have a figure. Now this is a coordinate A, B, C, D whose diagonal are intersecting at point A. So we need to prove that area of A, P, B that is this triangle area is equal to this triangle's area. And then to prove that area of A, P, B that is this into area of C, P, D is equal to area of P, D into area of B, P. So let's just start with our solution. Now what is given to us is AC, D is a coordinate. We need to prove that area of A, P, B into area of P, D is equal to area of P, D into area of B, P, C. For that we need to have a construction. We need to draw a pendicular to B, D, a pendicular to B, D. Like this. A, L, a pendicular to B, D, C, M, a pendicular to B, D. So now let's start with our proof. Now in triangle B, P, B we know that area of A, P, B will be equal to half into base that is B, P into altitude that is A, L. Let this be the first equation. Similarly area of C, P, D is equal to half into base that is P, D, P, D into altitude that is C, M. This is point M and this is point L. This be the second equation. Now multiplying equation 1 and 2 we have area of A, P, B into area of C, P, D is equal to half multiplied by half will give us 1 by 4 P, P into P, D into A, L into C, M. Again following the same procedure we can write down that area of triangle A, P, D multiplied by area of triangle B, P, C. Let's have a figure and see that will be equal to 1 by 4 into base of A, P, D, A, P, D is into altitude that is A, L into base of P, B, C, B, P, C that is this triangle is B, P into altitude is A, C, M. Further if you notice that the left inside are the product of the areas and the right inside are equal to each other. Since RHS of equation let's name it as 3 and 4 are equal therefore we can say that LHS are also equal that is area of A, P, B into area of C, P, D is equal to area of A, P, D into area of P, P, C. So this is the required answer that we need to prove since we have proved. This completes the session. Take care.