 Hello and welcome to the session. Let us understand the following question which says, in figure 6.53 ABD is a triangle right angle at A and AC perpendicular to BD, show that AB square is equal to BC into BD. Here we have the figure 6.53 in which ABD is a triangle right angle at A and AC is perpendicular to BD. Now let us first understand the theorem that we will be using in the question. It says, if a perpendicular is drawn from the vertex of the right angle of a right triangle, the hypotenuse, the triangles on each side of the perpendicular are similar to the whole triangle and to each other and this information is the key idea toward this question. Now let us proceed on to the solution. Here we can see in the figure that AC is perpendicular to BD. Now since AC is perpendicular to BD, therefore triangle ABC is similar to triangle ADC and each triangle is similar to triangle ABD by the above key idea. Therefore triangle ABC is similar to triangle ABD and also triangle ADC is similar to triangle ABD. We know that in similar triangles corresponding types are proportional. Therefore considering triangle ABC is similar to triangle ABD, we can write AB by BD is equal to BC by AB. Now on cross multiplication we get AB square is equal to BC into BD. Now which is our required answer? Hence proved. I hope you understood this question. That's all for the session. Bye and have a nice day.