Question

Draw two circles whose radii are $4.5cm$ and $3.5cm$ and the distance between their centres is $10.0cm$. Construct the common tangents to the circles and find the measure of the tangents.

Answer 1

Step 1: Draw a line AB = 10 cm
Step 2: Draw three circles
(i) Circle 'C1' with radius R = 4.5 cm and center as 'A'.
(ii) Circle 'C2' with radius r = 3.5 cm and center as 'B'.
(iii) Circle 'C3' with radius (R-r) = (4.5-3.5) = 1cm and center as 'A'.
Step 3: Draw a perpendicular bisector to AB. Mark the mid-point 'M' of line AB.
Step 4: With 'M' as center and 'AM' as radius construct a circle 'C4'. 'C4' cuts 'C3' at two points 'E' and 'F'.
Step 5: Join EB and FB. Now EB and FB are tangents to circle 'C3'.
Step 6: Join AE and AF. Extend AE to meet 'C1' at 'P' and AF to meet 'C1' at 'R'.
Step 7: Draw BQ || AP and BS || AR
Step 8: Join PQ and RS. PQ and RS are the required TANGENTS to circles C1 and C2.