CIRCLE (CDS)

Total Questions: 46

41. For a triangle, the radius of the circumcircle is double the radius of the inscribed circle, then which one of the following is correct?

Correct Answer: (c) The triangle is an equilateral
Solution:

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 = AY

Which one of the following is correct in respect of the above statements?

Correct Answer: (d) Statement I is incorrect and Statement II is correct
Solution:

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/2

Which one of the following is correct in respect of the above statements?

Correct Answer: (d) Statement I is incorrect and Statement II is correct
Solution:

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

Correct Answer: (d) None of the above
Solution:

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.

Correct Answer: (d) Neither I nor II
Solution:

46. In a ∆ABC, AB = BC = CA. The ratio of the radius of the circumcircle to that of the incircle is

Correct Answer: (a) 2 : 1
Solution: