 Hi and welcome to the session. Let us discuss the following question. Question says, in figure 6.61, two chords A, B and C, D intersect each other at point P. Prove that triangle A, P, C is similar to triangle D, P, B and second part is A, P multiplied by P, B is equal to C, P multiplied by P, P. This is the figure 6.61. Now let us start with the solution. In first part of the question, we have to prove that triangle A, P, C is similar to triangle D, P, B. So, we can write in triangle A, P, C and triangle D, P, B. Angle A, P, C is equal to angle D, P, B. These two angles are vertically opposite angles. So, they are equal. So, we can write angle A, P, C is equal to angle D, P, B. Now, if we see these two angles, these two angles are in the same segment of the circle and we know angles in the same segment are equal. So, we can say angle C, A, P is equal to angle P, D, B. Now, by A, A criteria of similarity we get triangle A, P, C is similar to triangle D, P, B. We know A, A criteria of similarity states that if two angles of one triangle are respectively equal to two angles of other triangle, then two triangles are similar. Now, this completes the first part of the question. Now, for second part, we know triangle A, P, C is similar to triangle D, P, B. This we have already proved above. We also know that in case of two similar triangles, the ratio of air-corresponding sides are equal. So, we can write A, P upon D, P is equal to C, P upon P, B. Now, multiplying both the sides of this expression by D, P into P, B we get A, P multiplied by P, B is equal to C, P multiplied by D, P. In the second part of the question, we were required to prove this only. So, this completes the session. Hope you understood the session. Take care and have a nice day.