Question

Draw a triangle ABC in which AB = 6 cm, BC = 4.5 cm and AC = 5 cm. Draw and label:

1. the locus of the centres of all circles which touch AB and AC,
2. the locus of the centres of all the circles of radius 2 cm which touch AB.
   Hence, construct the circle of radius 2 cm which touches AB and AC . 

Answer 1

Steps of construction:

1. Draw a line segment BC = 4.5 cm 
2. With B as centre and radius 6 cm and C as centre and radius 5 cm, draw arcs which intersect each other at A.
3. Join AB and AC.
   ABC is the required triangle.
4. Draw the angle bisector of ∠BAC
5. Draw lines parallel to AB and AC at a distance of 2 cm, which intersect each other and AD at O.
6. With centre O and radius 2 cm, draw a circle which touches AB and AC.