GEOMETRICAL PUZZLE - IV

Here is a geometrical puzzle of highschool level. Try to solve it.

There is a semicircular plot of land with radius R. A square garden is to be prepared in this semicircular region such that two vertices of the square are on the semicircular arc and remaining two vertices are on the diameter. What will be the area of the square in terms of radius R ?

If you get the answer then place it as a comment to my post. You require a Google registration for that. I will post the answer with solution on August 12.

SOME HUMOUR

• "Women are expert mathematicians. They always divide their age by two, multiply their husband's income by five and add a few years to the age of their friends !" (Einstein's opinion)
  
• Teacher : "What happens to gold when it is exposed to the air ?"
  Student : "It is probably stolen !"
  
• Did you hear about the Italian farmer who ran a steam roller across his fields because he wanted to market mashed potatoes?
  
  

SOLUTION TO GEOMETRICAL PUZZLE III

Here is the solution of geometrical puzzle III.

FUNNY MATHEMATICS

Have you ever tried to calculate the following ?

• 1111 x 1111
  
• 11111 x 11111 OR
  
• 111111111 x 111111111
  

Try it and you will get some funny numbers ! Let me give one for example...

111111111 x 111111111 = 12345678987654321

Isn't it funny ?

GEOMETRICAL PUZZLE-III

There are four circles each with radius 'r'. The circles are so arranged that each circle touches two of the remaining three. There is a big circle touching all four circles. What will be the radius of the bigger circle expressed in terms of 'r' ?

If you have an answer post it as a comment to this post. I will post the answer on 10th July.