**Exercise - 20 **

**1.** In the given figure, a circle touches all the four sides of a quadrilateral ABCD whose sides are AB = 6cm, BC = 7cm and CD = 4cm. Find AD.

**2.** In figure. l and m are two parallel tangents at A and B. The tangent at C makes an intercept DE between the tangent l and m. Prove that .

**3. **If all the sides of a parallelogram touch a circle, show that the parallelogram is a rhombus.

**4.** In figure, a circle is inscribed in a having sides AB = 12 cm, BC = 8cm and AC = 10cm. Find AD, BE and CF.

**5. **A circle is touching the side BC of a at P and is touching AB and AC when produced at Q and R. Prove that
AQ = ½ (Perimeter of )

**6. ** In figure. Two circles intersects each other at A and B. the common chord AB is produced to meet the common tangent PQ to the circle at D. Prove that DP = DQ.

**7.** In figure. XP and XQ are two tangents to a circle with centre O from a point X out side the circle. ARB is a tangent to the circle at R. prove that XA + AR = XB + BR.

**8. **A circle touches all the four sides a quadrilateral ABCD. Prove that the angles subtended at the centre of the circle by the opposite sides are supplementary.

**9.** If PA and PB are two tangents drawn from a point P to a circle with centre O touching it at A and B, prove that OP is the perpendicular perpendicular bisector of AB.

**Answers**

1. 3cm |
4. AD = 7cm, BE = 5cm, CF = 3cm |

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 |