Question

Construct an equilateral triangle of side $6cm$ and mark the incircle.

Answer 1

Step-1: Construct the equilateral triangle:

Draw a line segment $AB$ with $6cm$ and take that as base. Take $B$ as center and draw an arc with $6cm$ radius. Taking $A$ as center draw an arc with $6cm$ that should cut the previous arc. Name the intersection point as $C$ and connect it to $A,B$. Thus, equilateral triangle $ABC$ is formed.

Step- 2: Construct the angle bisector for $\angle CAB$:

Taking $A$ as center and with any radius draw an arc on the line segments $AB,AC$. From both the intersected points with same radius again draw arcs in the triangle. Both the arcs should bisect each other. Draw a line from $A$ to the opposite side through the intersection point and that is the angle bisector of $\angle CAB$

Step-3: Construct the center for incircle:

Two angular bisectors are needed to draw an incircle. So, draw another angular bisector for $\angle CBA$ by following the above procedure. Where the two angular bisectors meet name the point as $I$. That is the center for the incircle.

Step-4: Draw a perpendicular bisector from the point $I$:

Draw an arc with any radius and cut the line segment $AB$. From the intersection points taking more than the half the distance between the points draw an arc that should bisect each other. Name the point that the line meeting with segment $AB$ as $D$and connect the intersection point with $I$. $ID$ is the perpendicular bisector of line segment $AB$ from point $I$

Step- 5: Draw the incircle:

With $ID$ as radius and $I$ as center draw a circle that will be inscribed in the triangle. Thus, incircle is drawn with the given dimensions.

Hence, the required equilateral triangle is constructed and the incircle is drawn