CIRCLE THEOREMS

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CIRCLE THEOREMS. TANGENTS. A straight line can intersect a circle in three possible ways. It can be:. A TANGENT. A DIAMETER. A CHORD. B. O. O. O. B. A. A. A. 2 points of intersection. 2 points of intersection. 1 point of intersection. TANGENT PROPERTY 1. - PowerPoint PPT Presentation

Text of CIRCLE THEOREMS

  • CIRCLE THEOREMS

  • TANGENTSA straight line can intersect a circle in three possible ways.It can be:A DIAMETERA CHORDA TANGENT2 points of intersection2 points of intersection1 point of intersectionABOOOABA

  • TANGENT PROPERTY 1OA

  • TANGENT PROPERTY 2OAPB

  • OABP6 cm8 cmAP is a tangent to the circle.a Calculate the length of OP.b Calculate the size of angle AOP.c Calculate the shaded area.c Shaded area = area of OAP area of sector OABabExample

  • CHORDS AND SEGMENTSmajor segmentminor segmentA straight line joining two points on the circumference of a circle is called a chord.A chord divides a circle into two segments.

  • SYMMETRY PROPERTIES OF CHORDS 1OAB

  • SYMMETRY PROPERTIES OF CHORDS 2OABCDPQAB = CD

  • OFind the value of x.Triangle OAB is isosceles because OA = OB (radii of circle)ExampleABSo angle OBA = x.

  • THEOREM 1O

  • OFind the value of x.Angle at centre = 2 angle at circumferenceExample

  • OFind the value of x.Angle at centre = 2 angle at circumferenceExample

  • OFind the value of x.Angle at centre = 2 angle at circumferenceExample

  • OFind the value of x.Angle at centre = 2 angle at circumferenceExample

  • THEOREM 2O

  • OFind the value of x.Angles in a semi-circle = 90o and angles in a triangle add up to 180o.Example

  • THEOREM 3

  • Find the values of x and y.Opposite angles in a cyclic quadrilateral add up to 180o.Example

  • THEOREM 4

  • Find the value of x.Angles from the same arc in the same segment are equal.Example