Draw a transverse common tangent of length 8 cm to two circles of radii 4 cm and 2 cm and find the distance between the circles.

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10 cm

5 cm

8 cm

12 cm

answer is A.

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Detailed Solution

Given,
Radius of bigger circle

r_{1}

= 4 cm
Radius of smaller circle

r_{2}

= 2 cm
Length of transverse common tangent = 8 cm
Now make a line segment AB = 10 cm (which is calculated ahead)
Question Image

Make the bigger circle C1 with radius 4 cm from the point A as Centre.
Again, make a smaller circle C2 with radius 2 cm from the point B as center.
Here, sum of radius,
4+2= 6 cm
Now make another circle C3 with radius 6 cm from the point A as center.
Now, bisect the line AB from the midpoint M.
From this point M as Centre and AM as radius make an arc which cut the circle C3 at X. Here, BX = tangent to C3 Join XA to meet the bigger circle C1 at the point P
Make the line from point B parallel to APX.
Suppose this line cut the smaller circle C2 at point R.
Now make a line from point P to R.
Here, PR = transverse common tangent of length 8 cm.
So, from Pythagoras theorem,