 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that construct an equilateral triangle with one vertex A inscribed in a given circle with center O. Now let us start with its solution. Now here in this question we have to construct an equilateral triangle inscribed in a given circle with center O and one vertex of the triangle that is vertex A is lying on the circle as given. Now we shall discuss all the steps of construction one by one. Now to construct an equilateral triangle within this circle first we keep the compass at point O and then we measure the distance O A with the compass that is our first step is to measure distance O A with compass distance O A gives us the radius of the circle. Now with A as center and radius O A we draw an arc using our compass intersecting the circle at point B that is here with center A and radius O A we have drawn an arc intersecting the circle at point B. Now with center B and same radius we draw another arc which intersects the circle at point C. Now with center B and same radius that is equal to O A we have drawn another arc which intersects the circle at point C. Now again with center C and same radius that is equal to O A we draw another arc which intersects the circle at point D and now we will repeat the above step till we draw six such points on the circle and let us label the remaining points as E and F. Now we have labeled the points as B, C, D, E and F. Now we join alternate points that is point A to point C, point C to point E and point E to point A thus triangle A C E is the required equilateral triangle. This completes our session. Hope you enjoyed this session.