 Hi and welcome to the session. Let us discuss the following question. The question says, if circles are drawn taking two sides of a triangle as diameters, proof that the point of intersection of these circles lie on the third side. Let us now make a diagram to understand this question. We have drawn two circles with diameter A, B and A, C which are the sides of triangle A, B, C and these two circles intersect at point D and we have joined A and D. We have to prove that D lies on B, C. Let us first write down the given information. Two circles are drawn with sides A, B and A, C of triangle A, B, C as diameters. Both circles intersect point D. We have to prove that D lies on B, C. We have constructed and which joins A to D. Let us now begin with the proof. A, B is the diameter. Therefore, B is equal to 90 degree. This angle is equal to 90 degree because angle in a semicircle is the right angle. Let us name this equation as equation number one. Now, since A, C is a diameter, therefore angle A, D, C is equal to 90 degree because angle in a semicircle is a right angle. Let us name this equation as equation number two. On adding one and two, we get angle A, D, B plus angle A, D, C is equal to 90 degree plus 90 degree and this is equal to 180 degree. So, as angle A, D, B plus angle A, D, C is equal to 180 degree, therefore, B, D, C is a straight line. We have proved that D lies on B, C. This completes the session. Bye and take care.