CIRCLE (CDS)Total Questions: 4641. For a triangle, the radius of the circumcircle is double the radius of the inscribed circle, then which one of the following is correct?(a) The triangle is a right angled(b) The triangle is an isosceles(c) The triangle is an equilateral(d) None of the aboveCorrect Answer: (c) The triangle is an equilateralSolution:42. Let the incircle to a ∆ABC touch BC, AC and AB respectively at the points X, Y and Z.Statement I If AB > BC, then AB + AZ < BC + XC Statement II AZ = AYWhich one of the following is correct in respect of the above statements?(a) Statements I and II are correct and Statement II is the correct explanation of Statement I(b) Statements I and II are correct and Statement II is not the correct explanation of Statement I(c) Statement I is correct and Statement II is incorrect(d) Statement I is incorrect and Statement II is correctCorrect Answer: (d) Statement I is incorrect and Statement II is correctSolution:43. Let ABC be a triangle in which ∠ACB = 60° and AC = x < BC. Let the circle with centre at C and radius x meet BC at D. Let CF be the perpendicular drawn from C meeting AD at F.Statement I ∆ACD is isosceles but not equilateral. Statement II DF = x/2Which one of the following is correct in respect of the above statements?(a) Statements I and II are correct and Statement II is the correct explanation of Statement I(b) Statements I and II are correct and Statement II is not the correct explanation of Statement I(c) Statement I is correct and Statement II is incorrect(d) Statement I is incorrect and Statement II is correctCorrect Answer: (d) Statement I is incorrect and Statement II is correctSolution:44. A circle of radius 10 cm has an equilateral triangle inscribed in it. The length of the perpendicular drawn from the centre to any side of the triangle is(a) 2.5√3 cm(b) 5√3 cm(c) 10√3 cm(d) None of the aboveCorrect Answer: (d) None of the aboveSolution:45. AB and CD are two chords of a circle meeting externally at P. Then, which of the following is/are correct?I. PA PD = PC × PB II. ∆ PAC and ∆ PDB are similar.Select the correct answer using the codes given below.(a) Only I(b) Only II(c) Both I and II(d) Neither I nor IICorrect Answer: (d) Neither I nor IISolution:46. In a ∆ABC, AB = BC = CA. The ratio of the radius of the circumcircle to that of the incircle is(a) 2 : 1(b) 3 : 1(c) 3 : 2(d) None of theseCorrect Answer: (a) 2 : 1Solution:Submit Quiz« Previous12345