CIRCLE AND ITS RELATED TERMS

Circle is the set of all points in a plane that are equidistant from a given point in the plane known as the center of the circle.

Chord - is a segment whose endpoints lie on a circle

Secant - is a line that intersects the circle at two points

Diameter is the longest secant in a circle.

Tangent - is a line in the plane of the circle that intersects the circle at exactly one point 

Sector -The part of a circle enclosed by two radii  of a circle and an arc.

The cut piece of pizza is minor sector and the remaining is the major sector.

Segment -part of a circle bounded by a chord and an arc

Semi-circle - is an arc whose endpoints are endpoints of a diameter

Applications of Trigonometry in Real life

• Trigonometry is commonly used in finding the height of towers and mountains.

• It is used in navigation to find the distance of the shore from a point in the sea.

• It is used in oceanography in calculating the height of tides in oceans

• It is used in finding the distance between celestial bodies

• The sine and cosine functions are fundamental to the theory of periodic functions such as those that describe sound and light waves.

• Architects use trigonometry  to calculate structural load, roof slopes, ground surfaces and many other aspects, including sun shading and light angles

THE NUMBER 13

 Two interesting facts about the number 13: 

(i)  (1 / 13 )   =     0.076923076923076923076923...

                 (rational periodic infinite decimal)

On multiplying the periodic number 76923 by successive multiples of 13, the following curious numerical pattern is obtained.

76923 * 013 = 0999999
76923 * 026 = 1999998 
76923 * 039 = 2999997 
76923 * 052 = 3999996
76923 * 065 = 4999995

76923 * 078 = 5999994

76923 * 091 = 6999993

76923 * 104 = 7999992

76923 * 117 = 8999991

76923 * 130 = 9999990

 (ii) The numerical pattern abcabc is divisible by 13.

An interesting fact about the powers of 10

There seems to be only 11 powers of ten that are products of 2 integers without any zero digits.

10 ^ 0     =                      1 * 1

10 ^ 1     =                      2 * 5

10 ^ 2     =                      4 * 25

10 ^ 3     =                      8 * 125

10 ^ 4     =                      6 * 625

10 ^ 5     =                    32 * 3125 

10 ^ 6     =                    64 * 15625

10 ^ 7     =                  128 * 78125

10 ^ 9     =                  512 * 1953125 

10 ^ 18   =             262144 * 3814697265625 

10 ^ 33   =      8589934592 * 116415321826934814453125

CHOCOLATE PUZZLE

A shop sells chocolates @ Re.1 each. You can exchange 3 wrappers for 1 chocolate.


If you have Rs.15/- how many chocolates can you get totally????
 
 
Find the solution..
 
TO CHECK YOUR ANSWER ... SCROLL DOWN
 
 
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SOLUTION:
 
22 CHOCOLATES

 for  15 rupees you get 15 chocolates.
on returning 15 wrappers you get 5  chocolates.
on returning 3 wrappers  (keeping two wrappers in hand) you get 1 chocolate.
now this one  chocolate. wrapper and the twp wrapers you had will add on three.
atlast on returning 3 wrappers you get 1 chocolate.


i.e.,   15+5+1+1 = 22