Chapter 10.1, Problem 26WE

To determine

To construct: a triangle whose three angles are congruent to $\angle 1,\angle 2$ and $\angle 3$ and circumscribed circle has radius $r$ .

Explanation of Solution

Given Information:

Given figure,

  

Calculation:

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

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

Step 1: Construct an angle of $90°$ using protector.

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

Step 3: Join $A$ and $C$ by using ruler.

Step 4: Find the bisector of one of the triangle sides.

See constructing the perpendicular bisector of a line segment.

Repeat for the other side.

Step 5: The point where these two perpendiculars intersect is triangle’s circum center.

Step 6: Place the compasses point on the intersection of the perpendiculars.

Step 7: Set the compasses width to one of the points $A,B$ or $C$ . Draw a circle that will pass through all three.

  

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.