Q11 of 17 Page 173

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.


Steps of Construction:”

1. Draw a line segment AB of length 6cm.


2. With A as center, draw a circle of radius 1.7 cm.


3. With B as center, draw a circle of radius 2.8 cm.



4. With B as center, draw another circle of radius (1.7+2.8) =4.5cm.



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



6. With M as center and AM as radius draw a semicircle.



7. This circle intersects with circle of radius 5cm at S.


8. Join B to S. BS cuts the inner circle at K.



9. From A, draw a line parallel to BS.


10. This line intersects with the circle at L.



11. Join K to L.


12. KL is the required transverse common tangent.



More from this chapter

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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.

 10

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.

 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.

 2

Draw incircle of an equilateral triangle of side 4.6 cm. Do its circumcentre and incentre coincide with each other? Give reason for your answer