- Samer Seifeldeen
Consider the circle (C) with diameter[OB]. A is a point on the segment ]OB[. I mid point of [AB]. The perpendicular bisector of the segment [AB] cuts the circle at M and M' N orthogonal projection of A on (OM).
1) show that N,A and M' are collinear. Consider the direct plane similitude S of center N and transforms M onto A 2)a) precide the angle of this similitude b) Determine the image of the straight lines (MI) and (NA). c) Deduce the image of M' by S 3) a) Determine the image of I the midpoint of [MM'] b) Deduce that the straight line (NI) is tangent at N to the circle of diameter [OA]