Question

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

Draw and label:

(i) the locus of the centres of all circles which touch AB and AC,

(ii) the locus of the centres of all circles of radius 2 cm which touch AB.

Hence, construct the circle of radius 2 cm which touches AB and AC.

Answer 1

1

Steps of Construction:

i) Draw a line segment BC = 4.5 cm

ii) With B as centre and radius 6 cm and C as centre and radius 5 cm, draw arcs which intersect each other at A.

iii) Join AB and AC.

ABC is the required triangle.

iv) Draw the $\angle$ bisector of

v) Draw lines parallel to AB and AC at a distance of 2 cm, which intersect each other and AD at O.

vi) With centre O and radius 2 cm, draw a circle which touches AB and AC.