 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 AC square is equal to BC into DC. Given to us is figure where ABD is a right angle triangle at A and AC is perpendicular to BC. Now before writing the solution, let us see the theorem that we will be using in the question. Which states that if a perpendicular is drawn from the vertex of the right triangle, right angle of a right triangle to the high part of news, 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. Since in the given figure we can see AC is perpendicular to BD, therefore triangle ABC is similar to triangle ABC by the key idea. We know that in similar triangles corresponding sides are proportional. Therefore AC by BC is equal to BC by AC. Or we can write on cross multiplication AC square is equal to BC into DC. This is our required result, hence proved. I hope you understood the question. Bye and have a nice day.