 Hello and welcome to the session. Let us understand the following question today. ABC is an isosceles triangle with AC is equal to BC. If AB square is equal to twice of AC square, prove that ABC is a right triangle. Now before starting with the solution, let us understand the converse of Pythagoras theorem which states that if we have a triangle ABC in a triangle, ABC is given that AB square plus BC square is equal to AC square. Then we can say that angle B is equal to 90 degrees, that is triangle ABC is right-angled triangle. This is the key idea to our question. Now let us write the solution. Let us see the figure. ACB is a isosceles triangle with AC is equal to BC. Now let us write the solution. It is given that AB square is equal to twice of AC square. That is AB square is equal to AC square plus AC square. We can write AB square is equal to AC square plus BC square because given that AC is equal to BC as triangle ABC is an isosceles triangle. Therefore Pythagoras theorem is satisfied which implies triangle ABC is a right triangle hence proved. I hope you understood the question. Bye and have a nice day.