Answer :

Steps of Construction:”

1. Draw a line segment AB of length 8cm.

2. With A as center, draw a circle of radius 3 cm.

3. With B as center, draw a circle of radius 4 cm.

4. With B as center, draw another circle of radius (4-3) =1cm.

5. Draw a perpendicular bisector of AB. It intersects with AB at X.

6. With X as center and AX as radius draw a circle.

7. This circle intersects with circle of radius 1cm at P and Q.

8. Join B to P. Extend BP to R, a point on the outer circle.

9. Join B to Q. Extend BQ to S, a point on the outer circle.

10. From A, draw a line parallel to BR and another line parallel to BS.

11. These lines intersects with the circle at K and L.

12. Join K to R and L to S.

13. KR and LS are the required direct common tangents.

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