Q.Two circles of radii r1 and r2(r1>r2) touch each other both of them externally.Then what is the radius of the circle which touches both of them externally and also their direct common tangents.

the figure will be like three balls kept on a table( commen tangent) with the smallest circle between the two circles of radius r1 and r2. sorry i cant upload the image .

the solution is

the main idea is to find the distance b/w the foot of perpendiculars from the center of the two given circles to the common tangent by two ways and then equating the two equations obtained to get the value of radius.

1st equation

form a right triangle by taking the distance b/w the centers of the circles as hipotenuse and solve for the base using pythagores th.

2nd equation

form right angled triangles (2) by joining the centre of the required circle with the centres of the two given circles and solve for the base and then sum up the two distances and then equate it with the distance obtainesd in the first equation

R  =  r1+r2/( sq. root r1+ sq. root r2)square

hope you find it usefull

ATBSYA (all the best see you again)

Approved