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### Math Assignment Ch-10 Class X | Tangent to a circle

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__Tangent to a Circle__

*Maths assignment chapter 10 of class X. Maths assignment on tangent to the circle class 10th. Extra questions important for the CBSE examination for class X chapter 10.*Question 1: In the given figure the common tangents AB and CD to two circles intersect at E. Prove that AB = CD |

Question 2: PT and PQ are two tangents from external point P. If ∠PQT = 70 |

Question 3 |

Question 4 PQ and PR are tangents, SR ∥ PQ, ∠P = 30
^{o} then, Find ∠x [Ans 30^{o}] |

Question 5 CP, CQ and AB are three tangents to the circle. If CP = 11 cm, BR = 4 cm. Then a) Find BC [Ans 7 cm] b) Prove that : CP = (1/2) ✕ Perimeter of ABC c) Find the perimeter of the ABC [Ans 22 cm] d) Prove that : CA + AR = CB + BR e) Prove that : AB = AP + BQ f) If AC = 4 cm, AB = 5 cm, BC = 6 cm, then find CP [Ans 7.5 cm] |

Question 6 For the given figure answer the following questions a) If AB = 10 cm, AR = 7 cm, and RC = 5 cm, find BC [Ans 8 cm] b) If AB = 8 cm, BC = 10 cm, CA = 12 cm, then find AP, BQ and CR [Ans 7 cm, 5 cm, 3 cm] c) If AB = 8 cm, BC = 7 cm, CA = 5 cm, find BQ [Ans 5 cm] d) If AB = 8 cm, BC = 7 cm , CA = 5 cm, find the radius of the incircle [Ans √3] e) If AB = AC then prove that BQ = CQ |

Question 7 In △OPQ, OP =OQ = PQ = 6 cm, then find angle ∠PTQ |

Question 8 |

Question 9 PQ is the chord of length 6 cm of a circle of radius 6 cm, TP and TQ are tangents to the circle at point P and Q respectively. Find ∠PTQ. Also find the length TP. Ans [120 ^{o} , TP = √12 cm] |

Question 10 AP and BP are tangents. OA = 8 cm and OB = 5 cm. If AP = 15 cm, then find the length of BP. [Ans √264] |

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