TRICKY MATHS PUZZLES - PART

TRICKY MATHS PUZZLES – PART – I

Here in this blog we are discussing about TRICKY MATHS PUZZLES – PART – I . It is illustrated below :

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1. The bigger circle radius is 4 cm and the medium circle radius is 2 cm . The line tangent to all the circles and the three circles touch each other . Then what is the radius of the smallest circle ?

SOLUTION :

Let the radius of the bigger ( orange ) circle be 4 cm and the medium ( blue ) circle

be 2 cm

Here r is the radius of the smaller (red ) circle

The distance( X ) between the orange and the red circle will be obtained from having the distances (4 + r) and ( 4 – r ) and the corresponding distance ( Y ) blue and red circles from ( 2 + r ) and ( 2 – r )

By Pythagoras theorem , we have

X = √ ( 4 + r )² – ( 4 – r ) ²

= √ ( 16 + r² + 8r ) – ( 16 + r² – 8r )

= √ 8r + 8r = √ 16 r

X = 4√ r

Y =√ ( 2 + r ) ² – ( 2 – r ) ²

= √( 4 + r² + 4r ) – ( 4 + r² – 4r )

= √ 4r + 4r = √8 r

Y = 2 √2 r

x + y = √ r ( 4 + 2√ 2 )

Thus by Pythagoras theorem we get ,

6²= 2² + { (4 + 2√2 ) √r } ²