Question

Draw a right angled triangle ABC with AB = 4.5 cm, AC = 7.5 cm and ∠B = 90°. Construct the incircle. Write the steps of construction also.

Answer 1

Steps of Construction:

1. Draw AB = 4.5 cm.
2. At point B, construct ∠ABC = 90°.
3. With A as the centre and radius = 7.5 cm, draw an arc cutting the 90° line at point C. (Thus, AC = 7.5 cm.)
4. Join A to C. Triangle ABC is now constructed with ∠B = 90°.
5.  Bisect angle ∠A.
6. Bisect angle ∠C. The angle bisectors intersect at point I. Point I is the incentre of ΔABC.
7. Draw ID ⟂ AB. (From I draw a perpendicular to side AB. Let the foot of the perpendicular be D.) 
8. With centre I and radius = ID, draw a circle that touches all three sides of the triangle. This is the required incircle of ΔABC.
9. By measurement, ID gives the radius of the incircle.