Question

On your paper draw figures roughly like the ones shown. Then construct a triangle whose three angles are congruent to $\angle 1,\angle \text{2,}$ and $\angle 3$, and whose circumscribed circle has radius $r$.

Short answer

The figure is,

Step-by-step solution

Step 1. Given information.

Figures are given,

Step 2. Consider the following way.

The figure shows angles $1,2,3$ and the radius let $r=3cm$ as below,

By using these figure, the required $\Delta ABC$as below,

Construct an angle of $90°$using protector.

Cut off $BC=4cm$ and arc of $2cm$ from the other arm.

Join $A$ and $C$by using ruler.

Find the bisector of one of the triangle sides.

See constructing the perpendicular bisector of a line segment.

Repeat for the other side.

The point where these two perpendiculars intersect is triangle’s circum center.

Place the compasses point on the intersection of the perpendiculars.

Set the compasses width to one of the points $A,B$or $C$.

Draw a circle that will pass through all three.

Step 3. Construction.

The circle drawn is the triangle’s circumcircle, the only circle that will pass through all three of its vertices.

$\begin{array}{l}\angle A\cong \angle 3\\ \angle B\cong \angle 2\\ \angle C\cong \angle 1\end{array}$

Therefore, above is the circle having $r$as radius.