Question

Draw an equilateral Δ of sides 5 cm. Draw the circumcircle of it.

Answer 1

Steps of Construction:

1. Draw a line segment BC = 5 cm.
2. With B as centre and radius = 5 cm,
   draw an arc.
3. With C as centre and radius = 5 cm,
   draw another arc intersecting the first arc at point A.
   (Thus, AB = 5 cm and AC = 5 cm.)
4. Join A to B and A to C.
   Then △ABC is the required equilateral triangle.
5. Draw the perpendicular bisector of AB.
6. Draw the perpendicular bisector of BC.
7. The perpendicular bisectors intersect at point O.
   Therefore, O is the circumcentre of △ABC.
8. With O as centre and radius = OB (or OA or OC),
   Draw a circle passing through A, B, and C.
   This is the required circumcircle of the triangle.