Cyclic Quadrilaeral

Quadrilateral whose all the (four) vertius lie on a circle is called a cyclic quadrilateral.

**Theorem 4:-** The sum of the either pair of the opposite angle of a cyclic quadrilateral is 180^{0}

**Give: -** A cyclic quadrilateral ABCD

To prove:-

**Construction:-** Let O be the centre of the circle passing through A, B, C and D.
OB and OD are joined.

**Proof:-**

= x/2, say (Theo.2)

and

= y/2, say (Theo.2)

Adding (i) and (ii) we get

As the sum of the angles of a quadrilateral is 360

^{0}, there fore,

**Example 6.** In the adjoining figure,

**Solution:-** As BD = DC

ABCD is a cyclic quadrilateral.

Subjects |
Maths (Part-1) by Mr. M. P. Keshari |

Chapter 9 |
Circle |

Chapter 10 |
Tangents to a circle |

Chapter 11 |
Geometrical Construction |

Chapter 12 |
Troigonometry |

Chapter 13 |
Height and Distance |

Chapter 14 |
Mensuration |

Chapter 15 |
Statistics |

Chapter 16 |
Probability |

Chapter 17 |
Co-ordinate Geometry |