8. Construct any right angled triangle and draw incircle of that triangle. ∆ ABC is the required right angled triangle. Such that AB = 6 cm, BC = 9 cm and m ∠ABC = 90º,

Q8. Construct any right angled triangle and draw the incircle of that triangle.

To solve this problem, we will first construct a right-angled triangle based on specific measurements, and then construct its incircle (a circle touching all three sides of the triangle internally).

Step 1: Triangle Construction Details

Let \(\Delta ABC\) be the required right-angled triangle with the following dimensions:

• Length of side \(AB = 6 \text{ cm}\)
• Length of side \(BC = 9 \text{ cm}\)
• Angle \(m\angle ABC = 90^\circ\)

Rough Figure (Analytical Diagram)

Figure 1: Rough Sketch

Step 2: Steps of Construction

1. Draw a line segment \(BC\) of length \(9 \text{ cm}\).
2. At point \(B\), construct an angle of \(90^\circ\).
3. Cut off a segment \(AB\) of \(6 \text{ cm}\) from the ray of the \(90^\circ\) angle.
4. Join points \(A\) and \(C\) to form \(\Delta ABC\).
5. To find the incenter, draw the angle bisectors of \(\angle B\) and \(\angle C\).
6. Mark the point of intersection of these bisectors as \(I\) (the Incenter).
7. From \(I\), draw a perpendicular to side \(BC\) intersecting at point \(D\).
8. With \(I\) as the center and \(ID\) as the radius, draw a circle. This is the required incircle.

Final Construction

Figure 2: Final Construction