If necessary, review:

**Geometry with a Compass Practice Problems**

**PROBLEM 1**

Define a point by drawing a dot. Then, with the compass, draw a small circle centered on the dot. Now construct a second circle, concentric with the first one, but having twice the radius.

**SOLUTION 1**

Figure 5-5 illustrates the procedure. In drawing A, the circle is constructed with the compass, centered at the initial point (called point *P* ). In drawing B, a line segment *L* is drawn using the straight edge, with one end at point *P* and passing through the circle at a point *Q* . The line segment extends outside the circle for a distance considerably greater than the circle's radius. In drawing C, a circle is constructed, centered at point *Q* and leaving the compass set for the same radius as it was when the original circle was drawn. This new circle intersects *L* at point *P* (the center of the original circle) and also at a new point *R* . Next, the non-marking tip of the compass is placed back at point *P* , and the compass is opened up so the pencil tip falls exactly on point *R* . Finally, as shown in drawing D, a new circle is drawn with its center at point *P* , with a radius equal to the length of line segment *PR* .

**PROBLEM 2**

Draw three points on a piece of paper, placed so they do not all lie along the same line. Label the points *P, Q* , and *R* . Construct Δ *PQR* connecting these three points. Draw a circle whose radius is equal to the length of side *PQ* , but that is centered at point *R* .

**SOLUTION 2**

The process is shown in Fig. 5-6. In drawing A, the three points are put down and labeled. In drawing B, the points are connected to form Δ *PQR* . Drawing C shows how the non-marking tip of the compass is placed at point *Q* , and the tip of the pencil is placed on point *P* . (You don't have to draw the arc, but it is included in this illustration for emphasis.) With the compass thus set so it defines the length of line segment *PQ* , the non-marking tip of the compass is placed on point *R* . Finally, as shown in drawing D the circle is constructed.

**PROBLEM 3**

Can the non-marking tip of the compass be placed at point *P* , and the pencil tip placed to draw an arc through point *Q* , in order to define the length of line segment *PQ* in Problem 2?

**SOLUTION 3**

Yes. This will work just as well.

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