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Family Of Circles

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In this page we are going to discuss about family of circles.Here concentric circles plays a major role.First let us consider the definition of concentric circles.Two or more circles having same center is called the concentric circles.There are two types in family of circles. Circles touching each other: Two circles may touch each other either internally or externally. Circles touching each other externally: Here the center of two circles are C₁ and C₂ and radius are r₁ and r₂.The distance between their centers is sum of their radii. If the two circles are touching each other externally then they must satisfy the following condition.   C ₁ C ₂ = r ₁  + r ₂ Circles touching each other internally: Here the center of two circles are C₁ and C₂ and radius are r₁ and r₂.The distance between their centers is differences of their radii. If the two circles are touching each other internally then they must satisfy the following condition.   C ₁  C ₂ = r ₁  - r
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Centroid Of The Triangle

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In this page centroid of the triangle we are going to see the formula to find the centroid of any triangle. To find centroid we must given three vertices of the triangle.First let us see the definition of centroid. Definition: There are three medians of the triangle and they are concurrent at a point O,that point is called the centroid of a triangle. In the following diagram O is the centroid of ABC.Now let us look into the formula. Centroid of a triangle = (x1+x2+x3)/3, (y1+y2+y3)/3 Example 1: Find the centroid of a triangle whose vertices are the points (8,4)(1,3) and (3,-1). Solution: Centroid of a triangle is Centroid of a triangle = (x1+x2+x3)/3, (y1+y2+y3)/3 Here we have x1 = 8, x2 = 1and x3 = 3                    y1 = 4, y2 = 3 and y3 = -1                                   = (8 + 2 + 3)/3 , (4 + 3 -1)/3                                   = (12/3) , (6/3)                                   = (4,2) Therefore the centroid is (4,2) Examp
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TRIGONOMETRIC RATIOS OF COMPOUND ANGLES

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About "Trigonometric ratios of compound angles" Trigonometric ratios of compound angles : An angle made up of the algebraic sum of two or more angles is called a compound angle. Here, we are going see the formulas for trigonometric ratios of compound angles.  sin (A  + B )  =  sinA cosB + cosA sinB sin (A  - B )  =  sinA cosB - cosA sinB cos (A  + B )  =  cosA cosB - sinA cosB cos (A  - B )  =  cosA cosB + sinA cosB tan (A  + B )  =  [tanA + tanB] / [1 - tanA tanB] tan (A  - B )  =  [tanA - tanB] / [1 + tanA tanB] Trigonometric ratio table From the above table, we can get the values of trigonometric ratios for standard angles such as 0 °, 30 °, 45 °, 60 °, 90 ° Now, let us look at some practice problems on " Trigonometric ratios of compound angles". Trigonometric ratios of compound angles - Practice problems Example 1 : Find the value of cos15 ° Solution : First, we have to write the given angle 15 ° in terms of  sum or differ
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FORMULAS FOR SHAPES

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About the topic formulas for shapes  In this page formulas for shapes you can find many shapes and related formulas.Mensuration is one of the branches of mathematics.This means measurement.It is is being done in our life in many situations. For example, A length of cloth we need for stitching, the area of a wall which is being painted, perimeter of the circular garden to be fenced. For these kind of situation we need to use one of these formulas. Here, we cover two major areas. 1. Perimeter 2. Area Name of shape Formulas Circle Area of circle = Π r ² Circumference of circle =  2 Π r Equilateral Triangle Area of Equilateral-triangle = (√3/4) a² Perimeter of  Equilateral-triangle = 3a Scalene Triangle Area of scalene triangle = √s(s-a)(s-b)(s-c) Perimeter of scalene triangle = a + b +  c Semi circle Area of Semi circle= (1/2) Π r² Perimeter of semi-circle = Πr Quadrant Area of quadrant = (1/4) Π r² Parallelo
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BODMAS RULE

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About "BODMAS rule" What is BODMAS rule ? The rule or order that we use to simplify expressions in math is called "BODMAS" rule. Very simply way to remember  BODMAS rule!         B  ----->   Brackets first (Parentheses)        O  ----->   Of (orders :Powers and radicals)          D  ----->   Division        M  ----->  Multiplication        A  ----->  Addition        S  ----->  Subtraction Important notes : 1. In a particular simplification, if you have both  multiplication and division, do the operations one by one in the order from left to right. 2. Division does not always come before multiplication. We have to do one by one in the order from left to right.  3. In a particular simplification, if you have both  addition and subtraction, do the operations one by one in the order from left to right. Examples :  12 ÷ 3 x 5  =  4 x 5  =  20 13 - 5 + 9   =  8 + 9  =  17   In the above simplification, we have b
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