Similitude.MMG.ex9p323
- Author:
- 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]