What Is Segment Of A CircleSegment of a circle: The region enclosed by an arc and a chord is called the segment of the circle. Minor segment: If the boundary of a segment is a minor arc of a circle, then the corresponding segment is called a minor segm…

What Is Sector Of A Circle Minor sector: A sector of a circle is called a minor sector if the minor arc of the circle is a part of its boundary In Fig. sector OAB is the minor sector. Major sector: A sector of a circle is called a major sector if the ma…

How To Construct A Tangent To A Circle At A Given Point Steps of Construction Step I: Take a point O on the plane of the paper and draw a circle of given radius. Step II: Take a point P on the circle. Step III: Join OP. Step IV: Construct ∠OPT = 90º. St…

Fundamental Theorem of ArithmeticWe have discussed about Euclid Division Algorithm in the previous post.Fundamental Theorem of Arithmetic: Statement: Every composite number can be decomposed as a product prime numbers in a unique way, except for the orde…

Areas Of Two Similar TrianglesTheorem 1:  The ratio of the areas of two similar triangles are equal to the ratio of the squares of any two corresponding sides. Given: Two triangles ABC and DEF such that ∆ABC ~ ∆DEF. To Prove:  \(\frac{Area\ (\Delta ABC)}…

Solving Systems Of Equations By Elimination MethodStep I: Let the two equations obtained be a1x + b1y + c1 = 0                    ….(1) a2x + b2y + c2 = 0                    ….(2) Step II: Multiplying the given equation so as to make the co-efficients o…

Find The HCF And LCM using Prime Factorisation MethodRelation between two numbers and their HCF and LCM Consider two numbers 18 and 24. Prime factorisation of 18 = 2 × 3 × 3 Prime factorisation of 24 = 2 × 2 × 2 × 3 So, HCF = 2 × 3 = 6 LCM = 2 × 2 × 2 × …

Equations Reducible To A Pair Of Linear Equations ExamplesExample 1:    Solve the following system of equations \(\frac { 1 }{ 2x }\) – \(\frac { 1 }{ y }\) = – 1; \(\frac { 1 }{ x }\) + \(\frac { 1 }{ 2y }\) = 8 Sol.    We have, \(\frac { 1 }{ 2x }\) –…

Criteria For Similarity Of TrianglesAAA similarity criterion: If in two triangles, corresponding angles are equal, then the triangles are similar. AA Similarity criterion: If in two triangles, two angles of one triangle are respectively equal the two an…

Geometric Meaning Of The Zeroes Of A PolynomialLet us consider linear polynomial ax + b. The graph of y = ax + b is a straight line. For example : The graph of y = 3x + 4 is a straight line passing through (0, 4) and (2, 10). (i)   Let us consider th…