Question

Draw two circles with radii 2.5 cm and 4 cm and with their centres 7 cm apart.
Draw a direct common tangent and a transverse common tangent. Calculate the length of the direct common tangent. 

Answer 1

Steps of construction of transverse common tangent: 

(i) Draw a line OP= 7 cm. 

(ii) At O, draw a circle of radius 2. 5 cm. 

(iii) At P, draw a circle of radius 4 cm. 

(iv) At O, draw a third circle concentric to the smaller circle and radius= (2.5 + 4) cm= 6.5 cm 

(v) Draw a perpendicular bisector of OP. Let R be the mid-point of OP. 

(vi) With Ras centre and OR as radii, draw a fourth circle. Mark as T and S where the third and fourth cireles intersect each other. 

(vii) Join OT and OS to meet the smaller circle at A and B. 

(viii)Join PT and PS. 

(ix) On PT and PS, draw perpendiculars to meet the bigger circle at Mand N. 

(x) Join AM and BN. 

AM and BN are the required tangents. 

Steps of construction of direct common tangent: 

(i) Draw a line OP= 7 cm. 

(ii) At O, draw a circle of radius 4 cm. 

(iii) At P, draw a circle of radius 2.5 cm. 

(iv) At O, draw a third circle concentric to the bigger circle and radius = ( 42.5) cm= 1.5 cm 

(v) Draw a perpendicular bisector of OP. Let R be the mid-point of OP. 

(vi) With Ras centre and OR as radii, draw a fourth circle. Mark as T and S where the third and fourth cireles intersect each other. 

(vii) Join OT and OS and extend lines to meet the bigger cir de at A and B. 

(viii) Join PT and PS. 

(ix) On PT and PS, draw perpendiculars to meet the smaller circle at M and N. 

(x) Join AM and BN. 

AM and BN are the required tangents. 

On measuring, AM= BN = 7 cm.