Construct a `DeltaABC` with BC = 6.5 cm, AB = 5.5 cm, AC = 5 cm. Construct the incircle of the triangle. Measure and record the radius of the incircle.

Options

A. 1.6 CM
B. 2.3 CM
C. 2.7 CM
D. 1.9 CM

Answer

### Step-by-Step Solution

1. **Draw the Base BC**:
- Start by drawing a line segment BC that measures 6.5 cm. Label the endpoints as B and C.

2. **Construct Arc for AB**:
- Using a compass, measure 5.5 cm (the length of AB).
- Place the compass pointer at point B and draw an arc above the line segment BC.

3. **Construct Arc for AC**:
- Now, measure 5 cm (the length of AC) on the compass.
- Place the compass pointer at point C and draw another arc that intersects the first arc drawn in the previous step.

4. **Locate Point A**:
- Label the point where the two arcs intersect as point A. This completes the triangle ABC.

5. **Draw the Angle Bisector of Angle B**:
- To draw the angle bisector of angle B, place the compass pointer at point B and draw an arc that intersects both sides of the angle (lines AB and BC).
- Label the points where the arc intersects as D and E.

6. **Draw the Angle Bisector of Angle C**:
- Repeat the process for angle C. Place the compass pointer at point C and draw an arc that intersects both sides of the angle (lines AC and BC).
- Label the points where the arc intersects as F and G.

7. **Locate the Intersection of the Bisectors**:
- From points D and E, draw arcs with the same radius (more than half the distance between D and E) to find the intersection point.
- Do the same from points F and G. Label the intersection of these arcs as point O.

8. **Draw Perpendicular from O to BC**:
- From point O, draw a perpendicular line to line segment BC. Let the point where this perpendicular intersects BC be point D.

9. **Measure the Radius of the Incircle**:
- Use a ruler to measure the distance OD. This distance is the radius of the incircle.

10. **Draw the Incircle**:
- Set the compass to the length of OD. Place the compass pointer at point O and draw a circle. This circle is the incircle of triangle ABC.