In the adjacent figure,given:
_ C(o,3) is a circle of diameter {MN}
_A is point symmetrical to O about M
_{AY} is a semi_line tangent to (C) at T
1. show that triangle TOA is a semi equilateral triangle, and deduce the exact value of AT
2. reproduce the adjacent figure
3_ let (C¹) be the circke of diameter {AM}. (C) intersects {AY} in point E . show that (EM) //(parallel) to (TO) , then deduce that E is the midpoint of segment {AT}.
4. the tangent (d)to (C) at N , intersects {AY} in a point S . calculate AS and NS.
5. show that NTS is an equilateral triangle.
6. (TO) cuts (SN)in point K. show that (SO) is perpendicular to (KA)
