Wednesday, March 13, 2013

34-Problem on Circle 1


Dear Students,

I delivered the lecture on Mathematical Fun.  It was delivered in Indian Language “Marathi”. If you understand Marathi, Please click here to see my Lecture on youTube.

Secondly to think more about the studies of Mathematics, you are requested to participate in Program of Studies for Students and Parents given in my previous Blog. (Blog-11)

It is a problem from Student of 10th Standard / 10th grade. I would like to share the method of solving the problem & its presentation with you. Please go through it & make the habit of applying the same technique to solve other problems & please share this technique with your friends & relatives. (Please note one thing that “By distributing our knowledge, it will boost & by keeping it only with us, it will reduce”).
Please see the following Problem.

I found some easier method for this problem. so I would like to share this method with you. I am Sure, that you may also find some more easier method than this. so Please come forward to share your method also.

Two non-congruent circles touch each other externally. The sum of their areas is 298 π square centimeter and distance between there centers is 20 cm. Find the radii of both the circles.


1)    Let the radii of the circles be r1 & r2
2)    As the circles touch each other externally,  r1 + r2 = 20 cm
 So    r2 = 20 - r1
3)   Sum of areas of circles  = 298 π
So               π r12 + π r22 = 298 π
                           r12 + r22 = 298
            r12 + r22 + 2 r1 r2 - 2 r1 r= 298
                           (r1 + r2)2- 2 r1 r= 298     put (r1 + r2) = 20
                                (20)2- 2 r1 r= 298 
                                   (20)2- 298 = 2 r1 r2
 400- 298 = 2 r1 r2         Dividing Numerator &
                                        Denominator by 2
 200- 149 = r1 r2
            51 = r1 r2
          r1 r2 = 51            put the r2 = (20 - r1)
            r1 (20 - r1) = 51
             20 r1 - r12 = 51
     r12 - 20 r1 + 51 = 0
r12 - 17 r1 - 3 r1 + 51 = 0
    r1 (r1 – 17) – 3 (r1 – 17) = 0
     (r1 – 17) (r1 – 3) = 0
    So r1 = 17 or   r1 = 3
4)    So the radii of the circles are 17 cm & 3 cm.

Like this you can apply the technique to make use of simple calculations.

I hope, you will definitely implement this technique to save you valuable time of Examination or test. The same logical thinking can be applied to improve your thinking level.

I simply don't want to tell you to go with this simple method of calculation. I want that slowly, you need to mold yourself and improve the thinking level. Only using this technique for solving some problem and getting good scores will not serve my purpose. I want that the entire world need to improve the thinking skills so that every one can invent so many beautiful things of the human life.

This is possible only with the help of students like you along with your parents.

Please come ahead and start this beautiful work for yourself and show to the world that we can also build the world with powerful thinking level as every one is competent.

Anil Satpute