**Exercise - 21**

**Q. 1. **Two circles intersect at A and B. From a point P on one of these circles, two lines segments PAC and PBD are drawn intersecting the other circles at C and D respectively. Prove that CD is parallel to the tangent at P.

**Q. 2.** Two circles intersect in points P and Q. A secant passing through P intersects the circles at A an B respectively. Tangents to the circles at A and B intersects at T. Prove that A, Q, T and B are concyclic.

**Q. 3.** In the given figure. PT is a tangent and PAB is a secant to a circle. If the bisector of intersect AB in M, Prove that:
(i) (ii) PT = PM

**Q. 4.** In the adjoining figure, ABCD is a cyclic quadrilateral. AC is a diameter of the circle. MN is tangent to the circle at D, Determine

**Q. 5.** If is isosceles with AB = AC, Prove that the tangent at A to the circumcircle of is parallel to BC.

**Q. 6.** The diagonals of a parallelo gram ABCD intersect at E. Show that the circumcircles of touch each other at E.

**Q. 7.** A circle is drawn with diameter AB interacting the hypotenuse AC of right triangle ABC at the point P. Show that the tangent to the circle at P bisects the side BC.

**Answers**

4. 50^{0}, 75^{0} |

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 |