The Total solution for NCERT class 6-12
If circles are drawn taking two sides of a triangle asdiameters, prove that the point of intersection of these circles lie on thethird side.
Consider a╬ФABC.
Two circles are drawn while taking AB and AC as thediameter.
Let they intersect each other at D and let D not lie onBC.
Join AD.
тИаADB = 90┬░ (Angle subtended by semi-circle)
тИаADC = 90┬░ (Angle subtended by semi-circle)
тИаBDC = тИаADB + тИаADC = 90┬░ +90┬░ = 180┬░
Therefore, BDC is a straight line and hence, ourassumption was wrong.
Thus, Point D lies on third side BC of ╬ФABC.