Two concentric circles with integral radii are drawn with centre at point C. A chord PQ, 14 units in length, to the outer circle is also a tangent to the inner circle. What is the sum of the diameters of the two concentric circles?a)98 unitsb)49 unitsc)64 unitsd)IndeterminateCorrect answer is option 'A'. Can you explain this answer?

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a)
98 units
b)
49 units
c)
64 units
d)
Indeterminate

Correct answer is option 'A'. Can you explain this answer?

FREE This question is part of

IIFT Quantitative Ability MCQ Quiz - 2

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Two concentric circles with integral radii are drawn with centre at po...

The given data could be represented as shown in the above diagram.

Let R and r denote the radii of the outer and the inner circle respectively.
PQ is a tangent to the inner circle, hence it is perpendicular to the line joining the centre (C) of the inner circle and the point of intersection (T) of the circle and the tangent. Here, PT = TQ = 7

Also, ∠CTP =∠CTQ = 90°

In ΔCTP, CP₂= CT₂ + PT₂

R²= r²+ 7²

Thus, 7, r and R form a Pythagorean triple. 7 is part of only one such triplet, 7, 24 and 25.

r = 24,R = 25

Sum of the radii of both the circles = r + R = 24 + 25 = 49

The sum of the diameters of both the circles = 2 x 49 = 98

Hence, option 1.

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Two concentric circles with integral radii are drawn with centre at point C. A chord PQ, 14 units in length, to the outer circle is also a tangent to the inner circle. What is the sum of the diameters of the two concentric circles?a)98 unitsb)49 unitsc)64 unitsd)IndeterminateCorrect answer is option 'A'. Can you explain this answer?

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Two concentric circles with integral radii are drawn with centre at point C. A chord PQ, 14 units in length, to the outer circle is also a tangent to the inner circle. What is the sum of the diameters of the two concentric circles?a)98 unitsb)49 unitsc)64 unitsd)IndeterminateCorrect answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Two concentric circles with integral radii are drawn with centre at point C. A chord PQ, 14 units in length, to the outer circle is also a tangent to the inner circle. What is the sum of the diameters of the two concentric circles?a)98 unitsb)49 unitsc)64 unitsd)IndeterminateCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two concentric circles with integral radii are drawn with centre at point C. A chord PQ, 14 units in length, to the outer circle is also a tangent to the inner circle. What is the sum of the diameters of the two concentric circles?a)98 unitsb)49 unitsc)64 unitsd)IndeterminateCorrect answer is option 'A'. Can you explain this answer?.

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