Q10 of 17 Page 173

The centers of two circles of radii 3 cm and 4 cm are 8 cm apart. How many common tangents can be drawn to the two circles? Also, construct two direct common tangents to the circles.


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.



More from this chapter

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8

Draw a pair of tangents to a circle of radius 13.2 cm which are inclined to each other at an angle of 70°.

 9

Draw a circle of radius 3 cm. Take a point P at a distance of 5 cm from the center O of the circle from the point P, draw two tangents to the circle.

 11

The radii of two circles are 1.7 cm and 2.8 cm, and their centers are 6 cm apart. Construct a transverse common tangent to the two circles.

 1

Write the truth value (T/F) of each of the following statements. If possible, give reason for your answer.

(i) In an equilateral triangle, the incircle and the circumcircle can be constructed with the same centre.


(ii) The incircle of a triangle touches all sides of the triangle.


(iii) In an obtuse-angled triangle, the circumcenter lies on one of the sides of the triangle.


(iv) In an acute-angled triangle, the circumcentre lies inside the triangle.


(v) The incircle of a triangle is constructed by locating the point of intersection of perpendicular bisectors of any two sides of the triangle.