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Notes On Circle Questions

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Published in: IIT JEE Mains
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Some practice questions on circle

Pankaj J / Mumbai

4 years of teaching experience

Qualification: B.Tech/B.E. (IIT Delhi (IITD), Delhi - 2002), MBA/PGDM (ESCP Europe Paris - 2014)

Teaches: Algebra, Business Mathematics, Economics, Mathematics, Statistics, Physics, Science, KVPY Exam, AIEEE, BITSAT, IIT JAM, IIT JEE Advanced, IIT JEE Mains, BBA Entrance, BBA Subjects, Management Subjects, MBA Entrance

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  1. Consider a sequence {a }with al Test Paper 2 a n—l for all n > 3, terms of the sequence being an-2 42. distinct. If as are + ve integers and as < 162, then the possible value (s) of as can be 46. (B) (D) (B (A) 162 (C) 32 k If f(k) (C) bec=O 2017 r=l (B) 64 a then Paragraph for Question Nos. 49 and 50 Let ABCD is a rectangle with AB = a & BC = b & circle is drawn passing through A & B and touching side CD. Another circle is drawn passing though B & C and touching side AD. Let rl & rz be the radii of these two circle respectively. 49. 50. 62. equals a 4b a 4b (C) 2 2 2 b b a 4a a 4a b2 2 4b 2 —b2 Minimum value of equals 1 moves in such a way that the H.M. of a and b is 8. If c be the least area A variable line — + of triangle made by the line with the coordinate axis then the last digit of cc is
  2. 13. If inside a big circle exactly 24 small circles, each of radius 2, can be drawn in such a way that each small circle touches the big circle and also touches both its adjacent small circles, then radius of the big circle is + tan, (B) (D) 4. 8. 6. (A) 2 1+cosec 24 (C) 2 1+cosec 12 If + 9y2 + 25z (C) A.G.p. 2 24 cos — 24 2 sin — + COS — 15 5 3 = xyz , the x, y, 48 48 sin 24 z are in (D) H.Pe If the straight line 3x + 4y = 24 intersects the axes at A and B and the straight line 4x + 3y = 24 intersects the axis at C and D then the number of parabolas possible to draw through A, B, C and Two given circles of radii rl and rz touch each other externally. If the centre of a circle that touches both the circles externally is 3+205 then the locus of (A) a straight line (C) either of neo parabolas (B) a pair of perpendicular straight lines (D) a rectangular hyperbola A circle C Is tangent to the x and y-axis in first quadrant at the points P and Q respectively. BC and AD are parallel tangents to the circle with slope —1. If the points A and B are on the y—axis while C and D are on x-axis and area of figure ABCD is 90005 sq. units. The radius of the circle is (C) 30 (B) 6072 (D) 15
  3. 5. 8. 19. 25, Let al, a2, . . an be the terms of a G.P. whose common ratio is r. Set Sk denotes the sum of first k terms of the GP. then the value of in terms of Sm-l and Sm is sm_lSm sm Ism Curves ax2 + 2hxy + by2 — 2gx —2fy + c = 0 and a'x2 — 2hxy + (a' + a — b)y2 — 2g'x — 2fy + c = 0 g'+g f+f intersect at four concyclic points A, B, C and D. If P is the point the value of a'+a a'+a 2 is PD2 Which of the following condition must be satisfied so that two of the lines represented by the equation ay4 + by3x + cy2x2 + dyx3 + ax4 = O will bisect the angle between the other two? (A) b+d=O (B) bd=l The points A(3, 4) and B(4, 3) lies on same or opposite side of the line ax + by + c = O, (a, b, c E ) in which origin lies and PI and P2 are length of perpendicular from A and B to the line such that 2P1 + 3P2 = 10 then the line ax + by + c = O touches the circle (A) (x 18)2 + (y— 17)2 = 4 2 18 17 —4 5 5 2 18 17 4 5 5 Let Ll : 2x + 3Y+ p—3= 0 and 1-2 : 2x + 3Y+ p + 3 = 0 be lines and p E z. Let C : x2 + y2+ Ex + 10y + 30 = O, If it is given that at least one of the lines I-1 1-2 Is chord of C the probability that both are chords of C is 2 7 4 (C) 11 3 7 5 (D) 11
  4. 5. 4. 3. 5. 8. 81. The centres of the three circles A, B, and C are collinear with the centre of circle B lying between the centres of circle A and C circles A and C both touch externally to circle B and the three circles share a common tangent line. Given that circle A has radius 12 and circle B has radius 42 the radius of circle C, is equal to (A) 120 (C) 147 (B) 136 (D) 171 A diagonal of rhombus ABCD is a member of both the family of lines (x + y— 1) + i.1(2x + 3y — 2) = O and (x —y + 2) + Ä2(2x —3y+ 5) E R and one of the vertex of the rhombus is (3, 2). If area of the rhombus is 1206 square units then find the length of semi longer diagonal of the rhombus Let ABC be a triangle cwhose vertices are A(—5, 5) and B(7, —1). If vertex c has on a circle whose director circle has equation x2 + Y2 = 100, then locus of the orthocentre of triangle ABC is equal to (A) -8x -30=0 (D) x2 + y 2 + 4x + — 30 = O A circle passes through A(O, 4) and B(8, O) has its centre on x—axis. If point C lies on the circumference of the circle and m is the greatest area of triangle ABC, then m is equal to (c) 20 VS +1) (B) 10($+1) (D) 20 NE-I If the chord of contact of tangents from a point P to a given circle passes through Q then the circle on PQ as diameter -"tuts the given circle orthogonally (C) touches the given circle internally (B) touches the given circle externally (D) none of these Let two circles Cl and C2 of radii 2 and 4 be tangent at point P and tangent to a common straight line (not passing 'through P) at points Q and R, then value of PQ2 + QR2 + RP2 is. (1) 48 (2) 56 (3) 64
  5. 2 Consider three distinct lines x + icy + 6 0 2x + y— 3 — 0 let m denotes number of possible values of for which given lines are concurrent and n denotes number of possible values of for which given lines do not form a triangle, then An insect moves around the circle x2 + Y2 = 1 in circular orbits of different radii such that circle subtends an angle 9 to the insect where . Let Sl & S2 are circles with mmunum and 2 maximum radii of such orbits respectively, then the radius of locus of a point whose chord of contact to S2 touches Sl, is NS

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