Question 933144

1.
for constructions use only compass, straightedge (i.e. ruler) and a pencil

2. draw a large circle and a point {{{k}}} on not on the circle

since you need to construct a triangle that is circumscribe {{{about}}} a {{{circle}}}, means all three sides will touch a circle in one point; so, the sides of a triangle are {{{tangents}}} to a circle

and, use the fact that a tangent to a circle is perpendicular to the radius at the point of contact 
so, first create a radius of the circle, then construct a perpendicular to the radius at the given point {{{k}}}

how to construct it, step-by-step description is here:

http://www.mathopenref.com/printtangent.html


now, you got one perpendicular line, and you need second and third one:

choose another two points on a circle, repeat all procedure and construct second and third tangent, mark points of their intersection as, for example, {{{A}}},{{{B}}} and {{{C}}} and you will have a triangle {{{ABC}}} and the given point {{{k}}} will be on one of its sides


  

find the point where both tangents intersect; that will be