Before going to derivation, let us know some definitions related to triangles. Incircle: The circle that touches the three sides of a triangle internally is called ‘Incircle’ of that triangle. It is also called as ‘Inscribed circle’ . The centre and radius of this incircle are called incentre and inradius respectively. Incentre and inradius are denoted by ‘I’ and ‘r’ respectively. Inradius formula in terms of area and semi perimeter is r=∆/s . Where, ∆ is the area of triangle and s is the semi perimeter of triangle Derivation: Let us consider ∆ABC As shown in the above figure, let ‘I’ be the incentre and ‘r’ be the inradius. IF,ID, and IE be the perpendicular line segments drawn from I to AB,BC and AC respectively. Let the lengths of sides AB, BC, and AC be c, a and b respectively. Then semi perimeter = s = (a+b+c)/2 . Here we can write, Area of ∆ABC = A...
What to find : Locus of point from which tangents drawn to a circle have a particular angle (Angle not equal to zero) between them. Hello, Everyone. Before going to find our required solution, let us try to observe a phenomenon in the life. Figure : Illustration of variation of the angle with perpendicular distance from the wall Assumptions : Let us assume that a person X is standing in front of a wall shown in above figure. Assume height of the wall is more than the person. Let A, B and C be the different positions of eye of the person as the person moves on the horizontal line segment shown in the above figure. Let "O" be the point on the wall lying on the horizontal line segment drawn from the eye to the wall such that it is perpendicular to the wall. Let "E" be the one end of the wall as shown in the above figure. In the above figure, variation of the angle means variation of the a ngle between the horizontal line segment and line segment joining the eye ...
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