Question

Draw the circumcircle and incircle of an equilateral triangle XYZ with side 6.3 cm.

Answer 1

Steps of construction:
1. Draw a line segment XY = 6.3 cm.
2. With X as the centre and a radius of 6.3 cm, draw an arc.
3. With Y as the centre and the same radius as above, draw another arc cutting the previously drawn arc at point Z.
4. Join XZ and YZ.
5. Draw the perpendicular bisector of sides XY and XZ (any two sides) which intersect at I.
6. Taking IX or IY or IZ as radius, draw a circle which is the required circumcircle.
7. As we know that the perpendicular bisector is also the bisector of the angle in a equilateral triangle, I is also the point of intersection of the angle bisectors.
8. From point I, draw a perpendicular IK on side XY.
9. Taking IK as the radius, draw the required incircle.