HI GUYS

PLS HELP ME HOW TO CONSTRUCT A  PAIR OF DIRECT COMMON TANGENTLINES TO TWO CIRCLES IN THE FOLLOWING QUESTION:

THE CENTRES OF TWO CIRCLES OF RADII 2cm AND 3cmARE 7cm APART.DRAW A PAIR  OF COMMON TANGENT LINES TO THE TWO CIRCLES.

Following are the steps of construction of a  pair of common tangent lines to the two given circles:

1. Draw a line segment OO' of length 7 cm.

2. Draw a circle C₁ with centre O and radius 3 cm.

3. Draw another circle C₂ with centre O' and radius 2 cm.

4. Draw a perpendicular bisector to OO'.

5. Mark the point of intersection of OO' and perpendicular bisector as M.

6. Draw a circle C₃ with centre M and radius OM or OM'.

7. Draw another circle C₄ with centre O and radius equal to the difference of two radii of circles C₁ and C₂ i.e. (3 – 2) cm = 1 cm.

8. Mark the point of intersection of circles C₄ and C₃ as A and B.

9. Join OA and produce it to meet the circle C₁ at point P.

10. Join OB and produce it to meet the circle C₁ at point Q.

11. Draw a line parallel to OP from O' and mark the point of intersection of line and circle C₂ as R.

12. Draw another line parallel to OQ from O' and mark the point of intersection of line and circle as S.

13. Join PR and QS and produce them.

14. PR and QS are the required direct common tangents.

Cheers!