Circles

Circles

1. A circle is the locus of a curve A circle is the locus of a curve equidistant from a point .

   • Segment
   • Sector
   • Diameter
   • Arc
   • Radius
   • Chord

2. Theorems

   • Theorem 10.1 :- Equal chords of a circle subtend equal angles at the centre.
     • AB = CD  then  /_ AOB = /_ COD 
     • Theorems 10.2 :- If the angles subtended by the cord of a centre at the centre are equal, then the chords are equal .
       • /_ AOB = /_COD then AB=CD
       • Theorem 10.3 :- The perpendicular from the centre of a circle to a chord bisect the chord
         • OX _|_ AB then AX=AB
         • Theorem 10.4 :- The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord.
           • If AX=XB then OX_|_AB
           • Theorem 10.5 :- There is one and only circle passing through three given non-collinear points.
             • Theorem 10.6 :- Equal
             • Theorem 10.6 :- Equal chords of a circle are equidistant from the centre.
               • AB = CD then OX=OY
   • Theorem 10.7 :- Chords equidistant from the centre of a circle are equal in length.
     • OX = OY then  AB= CD
     • Theorem 10.8 :- The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
       • Reflex  then /_ POQ = 2/_PAQ
       • Theorem 10.9 :- Angles in the same segment of a circle are equal .
         • /_PAQ = /_ PBQ
         • Theorem 10.10 :- If a line segment joining two points subtends equal angles at two other points lying on the same side of the line continuing the line segment , the four points lie on circle.
           • /_ACB = /_ADB then A,B,C,D lie on the circle 
           • Theorem 10.11 :- The sum of either pair of opposite angles of a cyclic quadrilateral is 180° .
             • /_ A + /_C = 180° /_B + /_D = 180°
             • Theorem 10.12 :- If the sum of pair of opposite angles of a quadrilateral is 180° , then quadrilateral is cyclic .
               • if /_A + /_C = 180° , /_B + /_D  = 180°  then ABCD is a cyclic quadrilateral

3. MIND MAP

   • Created By : Name - Arindam Jana Class - 9  Sec. - F Roll - 04

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