Sunday, May 16, 2010

May 16, 2010

  1. The four circles of equal radius (say 1cm each)  are arranged in such a way that their centers make a perfect square, where each side of the square is 2cm long. What will be the dimension of the little circle that can be placed between all these four circles, such that the little circle just barely touches the four big circles. What is its area compared to the big circles?   (Lean More: Pythagoras Theorem).
  2. Actually it may be best that you try to draw the above figure using your geometry set. First draw the square, then the four circles, and if your drawing is perfect then the red circle will touch all the other four circles!
  3. How many numbers are there between 1 and 30, which are not prime, not a multiple of 4 or 5, and are  divisble by 2 and 6.
  4. Consider two points A and B which are at distance 5cm apart on the plane. Rotate A around B at each possible angle (300,270, 180, 90, 45, 30, ...).  Consider all the images of A. What shape they form?  What happens when A and B are in space - what does the angle of rotation means?
  5. In the previous problem - say A is a disc and B is a point. Then what shape the union of the images of B form?
  6. How many of the following statements are true? (a) The number of False statements are 1  (b) The number of False statements are 2  (c) The number of False statements are 3 (d) The number of False statements are 4.
  7. The sum of the ages of a couple is 77 years. Mr. He is now twice as old as Mrs. She was when he was as old as she is now. What are the current  ages of Mr. He and Mrs. She?
  8. How many pennies are there if in your pocket you have 50 coins making a change for a dollar?
  9. If 5 is added to 1/3rd of a number, it result in  1/2 of that number. Whats that number?
  10. How will you bisect an angle between two lines, without actually measuting the angle (you are allowed to use the compass).

1 comment:

  1. What about trisecting an angle?