मह्यम् dārśansūtra

Basic terminology of Mathematical Reasoning The sentences which are true or false but not both are called statements or mathematically acceptable statements.  The sentences which contains variable time, variable distances are not considered as statements. A sentence which is an exclamation, wish, imperative or interogative can't be a statement.  The statement which is true and false is represented by 'T' and 'F'.  Simple statement The statement whose true value is not depend on other statement is called simple statement.  Compound statement The statement which is combination of two or more simple statements are called compound statements.  Here, the simple statement which form compound statement are known as component statements.  Connectives AND (conjunction)  The connective 'and' will be true if both of its component statements are true.  OR (disjunction) The connective 'OR' will be true when any one of the component stat...

Radical axis Radical axis is a locus of a point from which length of tangent to two circles are equal.  Radical axis (geometric construction) In case of concentric circles radical axis does not exist.  If S ≡ x² + y² + 2gx + 2fy + c    S’ ≡ x² + y² + 2g’x + 2f’y+ c’ Then equation of radical axis of two circles. S = 0 and S’ = 0 is given by S = S’ x² + y² + 2gx + 2fy + c = x² + y² + 2g’x + 2f’y + c’ 2(g – g’)x + 2(f – f’)y + (c – c’) = 0 Radical centre Radical axis is always perpendicular to the line joining centres of the circle.  Radical axis of three circles whose centres are (non-collinear) taken in pair are always concurrency is called radical centre.  Radical centre is a point from which length of tangent to all three circles are equal.  Taking radical centre as centre and length of tangent equal to radius if we draw a circle then this circle is orthogonal to all three given circles.  Provid...