Summer Challenge 2008

 

 

This is the end of all challenge as Mr. Yue will concentrate on sharing of mathematics in Teaching and Learning webpage this year (2008 - 09).

Trigonometry Fun

Solution : Please Click Here

 

 

 

1.   In  DABC,  ÐC = 60o  and

            

     

If the area of the inscribed    circle of  DABC  is  12p cm2 , find the area of  DABC .

     

 

 

 

 

2.   In the figure above, ABCD is a straight line.

 

If  AB = BC = CD and  ÐBPC is a right angle,

prove that 

 

 

 

3.   Let  D  be the area of   DABC .

 

      It is given that:

                    .

 

      Show that  DABC  is right-angled.

 

 

 

4.   Brahmagupta's Formula

 

Brahmagupta (598–668) was an Indian mathematician and astronomer who discovered a neat formula for the area of a cyclic quadrilateral. Can you prove this?

 

If  D  is the area of a quadrilateral inscribed in a circle, prove that

 

 

where 

     

 

 

 

 

 

 

5.   Troublesome plane

 

ABCD  is a rectangular cardboard with sides  a = 4  and  b = 3 .

 

If  point  A  touches the horizontal ground,  point  B  is  1 unit  and point  C  is  2 units above the horizontal,  what is the angle between the cardboard and the horizontal ?

 

 

 

 

If you can solve any one or more question, you may send your solutions to me in WORD file by clicking here. Don’t forget to write down your name and class (and your school if you are not student of Queen’s College).  Deadline is 9 June 2008.  Solutions will be posted later.  There is no material prize. (The spiritual prize is the joy of learning mathematics.)