Construct a triangle ABC, with AB = 5.6 cm, AC = BC = 9.2 cm. Find the points equidistant from AB and AC, and also 2 cm from BC. Measure the distance between the two points obtained.

Answer

### Step-by-Step Solution:

1. **Construct Triangle ABC**:
- Draw a line segment AB = 5.6 cm.
- Label the endpoints as A and B.

2. **Construct Arcs to Find Point C**:
- Using a compass, set the radius to 9.2 cm.
- With center A, draw an arc above and below line AB.
- Without changing the compass width, place the compass at point B and draw another arc that intersects the first arc.
- Label the intersection point as C.

3. **Join Points to Form Triangle ABC**:
- Draw line segments AC and BC to complete triangle ABC.

4. **Draw Parallel Lines to BC**:
- Measure 2 cm from line BC and draw two parallel lines (one above and one below BC). Label these lines as M and N.

5. **Construct the Angle Bisector of ∠BAC**:
- Using a compass and straightedge, construct the angle bisector of angle BAC. This will divide the angle into two equal parts.

6. **Identify Points P and Q**:
- Extend the angle bisector until it intersects line M at point P and line N at point Q.

7. **Measure the Distance between Points P and Q**:
- Use a ruler to measure the distance PQ. This is the distance between the two points obtained.

### Final Result:
- The distance between points P and Q is found to be 4 cm.