Question

how to construct a circle in equilateral triangle

Answer 1

take the radius of side of triangle and take the centre of triangle and draw the circle

Answer 2

1.Draw a straight line segment.
2.Then take a line segment of equal length.
3.From the two ends of the drawn straight line, take a compass and cut off their bisectors.
4.Join all the lines and here you go with an equilateral triangle.

For inscribed circle as requested in the comments :-
1.After the circle is drawn,
From the two ends draw a complete arc on both sides.
2.From the two points on the triangle which the arc touches, draw the bisectors and then point out the point of intersection.
3.Now the downwards draw an arc and you would be see again two points on the line segments.
4.From these two points, again draw a bisector.
Now from the point where the bisector and point of intersection meets, take the compass there and then stretch it till the line segment.
5.Then draw a circle simply and you will find it inscribed.

HOPE THIS HELPS!!!