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?

EduRev

All Courses

Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity

Open App

CAT Exam > CAT Questions > Two concentric circles with integral radii ar...

Join the Discussion on the App

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

Attempt Test

Attempt this Test

Verified Answer

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.

View all questions of this test

View all answers Start learning for free

< Previous Question Next Question >

Explore Courses for CAT exam

Similar CAT Doubts

In the adjoining figure, I and II are circles with centres P and Q, respectively. The two circles touch each other and have a common tangent that touches them at points R and S, respectively. This common tangent meets the line joining P and Q at O. The diameters of I and II are in the ratio 4 : 3. It is also known that the length of PQ is 28 cm.What is the ratio of the length of PQ to that of QO?

View answer

In the figure given below AG and BG are diameters of two circles with radii 2 cm and 6 cm respectively. G is the only point of contact of the two circles. BC is a tangent of length 12 cm to the bigger circle and BF is perpendicular to the line AC. Find the length of CF.

View answer

Circles with radius of 6 units and 4 units are drawn in such a way that exactly 3 common tangents are possible. If a direct common tangent from point A touches the circles at points B and C, what is the length of BC?

View answer

Three horses are grazing within a semi-circular field as shown in the diagram and AB is the diameter of the semi-circular field with centre at O. The horses are tied up at P, R and S such that PO and RO are the radii of semicircles with centres at P and R, respectively and S is the centre of the circle touching the two semi-circles with diameters AO and OB. The horses tied at P and R can graze within the respective semi-circles and the horse tied at S can graze within the circle centred at S. What is the percentage of area of the semi-circle with diameter AB that cannot be grazed by the horses?

View answer

For 2 Concentric circles, a chord of the larger circle is a tangent to the smaller circle. If the chord length is 16 cm and radius of the smaller circle is 6 cm, what is the radius of the larger circle?

View answer

Top Courses for CATView all

Quantitative Aptitude (Quant)

Crash Course for CAT

CAT Mock Test Series 2024

3 Months Preparation for CAT

CAT Mock Test Series and 500+ Practice Tests 2024

Top Courses for CAT

View all

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?

Share with a Friend

Answer this doubt

Question Description
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?.

Solutions 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? in English & in Hindi are available as part of our courses for CAT. Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.

Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of 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?, a detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an ample number of questions to practice 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? tests, examples and also practice CAT tests.

Explore Courses for CAT exam