question_answer

Draw a line segment AB of length 7 cm. Taking A as centre, draw a circle of radius 3 cm and taking B as centre, draw another circle of radius 2 cm. Construct tangents to each circle from the centre of the other circle.

Answer:

Steps of construction:

(i) Draw a line segment \[AB=7\text{ }cm\].

(ii) Take A as centre, draw a circle of radius 3 cm.

(iii) Take B as centre, draw a circle of radius 2 cm.

(iv) Bisect AB at O.

(v) Draw a circle with O as centre and radius equal to AO (= OB) to intersect the circle of radius 3 cm at P and P?, and the circle of radius 2 cm at Q and Q'.

(vi) Join BP and BP?. Also, join AQ and AQ'.

Then, BP, BP', AQ and AQ' are the required tangents.