Construct the incircle of the triangle ABC below - Leaving Cert Mathematics - Question a(i) - 2014

To construct the incircle of triangle ABC, follow these steps:

1. Draw the Triangle: Start by accurately sketching triangle ABC on your paper.

2. Locate the Angle Bisectors: Use a compass to bisect each angle of the triangle. To do this for each angle:

   • Place the compass point on vertex A, draw an arc that intersects both sides of the angle.
   • Without changing the compass width, place the compass on each intersection to draw arcs, creating an intersection point.
   • Draw the angle bisector from vertex A through this intersection point.
   • Repeat for angles B and C.

3. Find the Incenter: The point where all three angle bisectors intersect is the incenter, denoted as point I. Mark this point clearly on your diagram.

4. Draw the Incircle: Using a compass, set the width to the distance from point I to any side of the triangle. Draw a circle that touches all three sides of triangle ABC. Ensure that the circle is tangent to each side and clearly show all construction lines.

5. Finalization: Label the incenter I and make sure all construction lines and angles are clear.