 Hello and welcome to the session. The question says in figure 1, angle BAC is 90 degrees. Also AD is perpendicular on BC. We have to prove that AB square plus CD square is equal to BD square plus AC square. Let's start with the solution. Here we are given first that angle BAC is equal to 90 degrees and also we are given that AD is perpendicular on BC. So this implies that angle BDA is equal to angle CDA is equal to 90 degrees. Now let us consider triangle ADC. So this implies this triangle we have AC square is equal to AD square plus DC square this is by Pythagoras theorem and also in triangle ADB we have AB square is equal to AD square plus BD square and this is again by Pythagoras theorem which says in a right triangle the square of the hypotenuse is equal to the sum of the square of the two sides. Let us denote this by equation number 1 and this by equation number 2. Now subtracting 1 from equation number 2 we have on the left hand side AB square minus AC square on right hand side we have AD square plus BD square minus AD square plus DC square or we further have AB square minus AC square is equal to BD square minus DC square or we have AB square plus DC square is equal to AC square plus BD square or it can also be written as AB square plus CD square is equal to BD square plus AC square and this is what we are required to prove. So this completes the session by intake cure.