 Hello and welcome to the session. Let us understand the following question today. p q r is a triangle right angle at p and m is a point on q r, so that p m is perpendicular to q r. Show that p m square is equal to q m multiplied by m r. Now, before writing the solution, let us understand the theorem that we will be using in our question. It states 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. And this is the key idea to our question. Now, let us write the solution. Now, we will draw a triangle p q r, right angle at p and m is a point on q r such that p m is perpendicular to q r. Here is a right angle triangle p q r which is right angle at p and m is a point on q r such that p m is perpendicular to q r. Now, we know in similar triangles corresponding sides are proportional. So now, m is perpendicular to q r. Therefore, triangle p r m thus p r m is similar to triangle q p m by our key idea which implies divided by m r is equal to q m by p m which implies on cross multiplication p m multiplied by p m is equal to m r multiplied by q m which implies p m square is equal to q m into m r. And this is the required result. I hope you understood the question. Bye and have a nice day.