 Hello and welcome to the session. Let us understand the following question today. In figure 6.53 ABD is a triangle right angle at A and AC is perpendicular to BD. Show that AD square is equal to BD into 3D. Now let us see the figure. We have figure with ABD is a triangle right angle at A and AC is perpendicular to BD. So before writing the solution let us see the theorem we will be using in the question. Which state that if a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse the triangles on each side of the perpendicular are similar to the whole triangle and to each other. This is the key idea to our question. Now let us write the solution. We can see that AD AC is perpendicular to BD. Therefore triangle ACD is similar to triangle ABD by key idea. Therefore we know that in similar triangles corresponding sides are proportional. Therefore AD by DC is equal to BD by AD. On truss multiplication we can write AD square is equal to BD into CD. This is our required result. Hence proved. I hope you understood the question. Bye and have a nice day.