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

Mathematics Assignment Class X

Tangent to a Circle  Chapter 10

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 = 70o, Find ∠x [Ans 20o]

Question 3 AB is the chord of the circle with centre O, AOC is the diameter and AT is the tangent at A. Prove that . ∠1 = ∠2

Question 4 PQ and PR are tangents, SR ∥ PQ,  ∠P = 30o then,  Find ∠x        [Ans 30o] Hint: ∠RQP = ∠PRQ  = 75o ∠RQP = ∠S =  75o    (∵ Angles in the alternate segments are equal) ∠S + ∠x + ∠RQP = 180o

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 In △ABC, AC = 8 cm, AB = 6 cm, ∠A = 90o, find the radius of the circle. [Ans 2cm]

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 [120o , 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]

Question 11 In the given figure find the length of AB and AC Ans [AB = 7.5, AC = 6.5 cm]

Question 12 ∠D = 90o , BC = 38 cm, CD = 25 cm, and BP = 27 cm, find radius r of the circle. [Ans 14 cm]

Question 13 O is the centre of the circle of radius 5 cm. T is a point such that OT = 13 cm and OT intersect the circle at E. If AB is the tangent to the circle at E, then find the length AB  [Ans 20/3] Hint :-        AT2  =  AE2 + ET2            (PT - AE)2  =  AE2  + ET2              (12 - AE)2 = AE2 + 82

Question 14 A chord PQ of a circle is parallel to the tangent drawn at a point R of the circle. Prove that point R bisects the arc PRQ.

Question 15 The lengths of three consecutive sides of a quadrilateral circumscribing a circle are 4 cm, 5 cm, and 7 cm respectively. Find the length of the fourth side. [Ans 6 cm] Hint: x + y = 4 ….(i) Y + z = 5 …(ii) a + z = 7 ….(iii) Adding (i), (ii), (iii) we get: x + 2y + 2z + a = 16 ......(iv) Eqn.(iv) – 2 X Eqn (ii) : x + a = 6 OR Sum of opposite sides are equal AB + CD = BC + DA 4 + 7 = 5 + x ⇒  x  = 11-5 = 6

Question 16 From an external point p, two tangents PA and PB are drawn to the circle with centre O. Prove that OP is the perpendicular bisector of AB

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