To inscribe a circle in the triangle, we have to find it's incenter.
Practice makes perfect
Copying the triangle
To copy the triangle, we can use the SAS Congruence Theorem. By copying the horizontal side, the smallest of the triangle's sides, and the included angle, we can draw a congruent triangle. Let's measure the horizontal side and the smallest of the triangle's sides.
Horizontal side:& 4.1 cm
Smallest side:& 2.7 cm
We will start by drawing the horizontal side along the x-axis.
Using a protractor, we can measure an angle of 55^(∘).
Now we can draw the smallest side, AC, using a ruler.
By connecting B and C, we have copied the triangle.
To inscribe a circle, we have to find the triangle's incenter. We can do that by drawing angle bisectors for at least two of the triangle's vertices. The point where the angle bisectors intersect is the triangle's incenter.
Finding the incenter
Let's start by drawing the angle bisector of ∠ B. First, we will draw an arc across AB and BC with an arbitrary radius like below.
Next, we draw two smaller arcs using the intersections of the first arc with AB and BC as our centers. Make sure you keep the compass settings the same for both of them.
The segment from B and through the intersection point of the two smaller arcs is the angle bisector to ∠ B.
We need one more angle bisector to find the incenter. Let's repeat the procedure for ∠ A.
Where the angle bisectors intersect, we find the triangle's incenter. Let's isolate this in our diagram.
To inscribe a circle, we also need to find the perpendicular bisector from the incenter and one of the triangle's sides. Let's do that with AB.
Finding a perpendicular bisector
We have to draw an arc that intersects AB as well as two smaller arcs using the intersections of the first arc with AB as our centers. Make sure you keep the compass settings the same for the two smaller arcs.
The segment from D to the intersection of the two smaller arcs is the perpendicular bisector.
Let's limit the perpendicular bisector to DE.
Constructing the inscribed circle
Finally, we will place the compass at D and set it's width to DE. Now we can construct the inscribed circle.
