 Hello and welcome to the session. Let us discuss the following question. It says in figure 1 angle ACB is 90 degrees, CD is perpendicular to AB. Prove that CD square is equal to BD into AD. Let's now move on to the solution. And let's first write what is given to us. We are given that in triangle ABC angle ACB is 90 degrees and CD is perpendicular to AB. Let's now write what we have to prove. We have to prove that CD square is equal to BD into AD. And to prove this, we will prove that triangle BCA is similar to triangle DBC so that the ratio of their corresponding sides will be equal and we will get the required result. So let's now start the proof. Now angle is equal to angle CDB. CDA is equal to angle CDB because each is 90 degrees. And also angle that is this angle is equal to angle CBD. This is because triangle is similar to triangle ACB that is this triangle is similar to this whole triangle. And this is because angle DC is equal to angle ACB because each is 90 degrees. This angle is 90 degrees and this angle is 90 degrees. Also angle is equal to angle CAB because this is a common angle is equal to angle CAB. Angle ACD is similar to triangle ACB by AA similarity. Angles of the two triangles are equal and third angle will also be equal to one another. So angle ACD is equal to angle CBD. So this implies triangle DA is similar to triangle. Since the triangles are similar, the ratio of their corresponding sides will be same. So DC upon DA is equal to DB upon DC that is CD upon AD is equal to VD upon CD cross multiplying we have CD square is equal to VD into AD. Hence the result is proved. Please the question and the session by for now take care have a good day.