Circle Introduction PDF

Circle 🔴 What is a Circle? Circle: When a line segment is rotated about one of its end point, then the curve traced by the other end point is called a circle, where, the fixed point about which rotation is done is called its centre & the length of line segment is called its radius. Circle Repre...

Circle 🔴 What is a Circle? Circle: When a line segment is rotated about one of its end point, then the curve traced by the other end point is called a circle, where, the fixed point about which rotation is done is called its centre & the length of line segment is called its radius. Circle Representation: Concept to cover in this chapter A)Secant B)Chord C)Tangent D)Length of tangent E)Common tangent F)Length of common tangent G)Important theorems H)Questions Position of st. Line w.rt to Circle :-  Difference between chord and secant Chord secant 1. It is a line segment. 1. It is a line. 2. All part of its lies inside the 2. Some part of it lies inside & Some circle. part outside the circle. Similarity:-one can be defined from other so both intersects the circle at 2 points. Position of points w.r.t circle Tangent and it’s length :- Common tangent and length of a common tangent Theorem 1. Prove that a tangent to a circle is perpendicular to the radius through the point of contact A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 13 cm. Find the length of PQ. Theorem 2. Prove that a line drawn through the end point of a radius and perpendicular to it is a tangent to the circle. Theorem 3. Prove that the lengths of two tangents drawn from an external point to a circle are equal. Theorem 4. Prove that, If two tangents are drawn to a circle from an external point, then: (i) They subtend equal angles at the centre, (ii) They are equally inclined to the segment, joining the centre to that point.  Concept and question Show that tangent lines at the end points of a diameter of a circle are parallel. Concept and question Prove that a diameter AB of a circle bisects all those chords which are parallel to the tangent at the point A. Concept and question In figure, if AB = AC, prove that BE = EC. Or ABC is an isosceles triangle in which AB = AC, circumscribed about a circle, then, Prove that the base is bisected by the point of contact..  Concept and question A circle is touching the side BC of AABC at P and touching AB and AC produced at Q and respectively. Prove that AQ = 1/2 (Perimeter of ∆ABC).