Draw a triangle $A B C$ in which $A B = 6 c m, B C = 4.5 c m$ and $A C = 5 c m$ . Draw and label:
(i) the locus of the centres of all circles which touch $A B$ and $A C$ ,
(ii) the locus of the centres of all the circles of radius $2 c m$ which touch $A B$ .
Hence, construct the circle of radius $2 c m$ which touches $A B$ and $A C$ .

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Solution

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 ∠BAC
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.

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