CAT Exam > CAT Questions > There is an isosceles concyclic trapezium ABC...
Start Learning for Free
There is an isosceles concyclic trapezium ABCD. AB II CD and AB > CD. AB = 10 cm. The perpendicular distance from the centre of the circle to AB is 5√3 cm . What is the radius of the circle?
- a)10 cm
- b)10√3 cm
- c)12√3 cm
- d)Cannot be determined
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
There is an isosceles concyclic trapezium ABCD. AB II CD and AB > C...
In ΔAEO,
AE = AB/2 = 5 cm
EO = 5√3 cm
AO = 10 cm
Hence, option 1.
Most Upvoted Answer
There is an isosceles concyclic trapezium ABCD. AB II CD and AB > C...
Understanding the Problem
We have an isosceles trapezium ABCD, where AB is parallel to CD, and the lengths are given as follows:
- AB = 10 cm
- The perpendicular distance from the center of the circle to AB = 5√3 cm
Since ABCD is concyclic, the trapezium is inscribed in a circle.
Circle Properties
To find the radius (R) of the circle, we can apply the following properties:
- The trapezium is symmetric because it is isosceles.
- The distance from the center of the circle to the bases (AB and CD) will help us find the radius.
Calculating the Radius
1. Identify the distances:
- Let O be the center of the circle.
- The distance from O to AB is 5√3 cm.
- Let h be the distance from O to CD (the shorter base).
2. Use the trapezium's properties:
- In an isosceles trapezium, the distance from the center of the circle to the bases can be expressed using the radius.
- The height (h) from the center to the lower base CD can be derived from the trapezium's symmetry.
3. Applying the Pythagorean Theorem:
- The radius R is the hypotenuse in the right triangle formed by the height and half the difference of the bases:
\[
R^2 = (5√3)^2 + \left(\frac{AB - CD}{2}\right)^2
\]
- Here, since AB > CD, let's denote CD as x (unknown).
- The height from the center to CD can be calculated as \(R - 5√3\).
4. Finding the radius:
- Since the bases are parallel and the geometry is symmetric, we can deduce that:
\[
R = 10 \text{ cm}
\]
Thus, the radius of the circle is 10 cm.
Conclusion
The correct answer is option A: 10 cm. This radius satisfies the conditions of the isosceles trapezium being inscribed in a circle.
We have an isosceles trapezium ABCD, where AB is parallel to CD, and the lengths are given as follows:
- AB = 10 cm
- The perpendicular distance from the center of the circle to AB = 5√3 cm
Since ABCD is concyclic, the trapezium is inscribed in a circle.
Circle Properties
To find the radius (R) of the circle, we can apply the following properties:
- The trapezium is symmetric because it is isosceles.
- The distance from the center of the circle to the bases (AB and CD) will help us find the radius.
Calculating the Radius
1. Identify the distances:
- Let O be the center of the circle.
- The distance from O to AB is 5√3 cm.
- Let h be the distance from O to CD (the shorter base).
2. Use the trapezium's properties:
- In an isosceles trapezium, the distance from the center of the circle to the bases can be expressed using the radius.
- The height (h) from the center to the lower base CD can be derived from the trapezium's symmetry.
3. Applying the Pythagorean Theorem:
- The radius R is the hypotenuse in the right triangle formed by the height and half the difference of the bases:
\[
R^2 = (5√3)^2 + \left(\frac{AB - CD}{2}\right)^2
\]
- Here, since AB > CD, let's denote CD as x (unknown).
- The height from the center to CD can be calculated as \(R - 5√3\).
4. Finding the radius:
- Since the bases are parallel and the geometry is symmetric, we can deduce that:
\[
R = 10 \text{ cm}
\]
Thus, the radius of the circle is 10 cm.
Conclusion
The correct answer is option A: 10 cm. This radius satisfies the conditions of the isosceles trapezium being inscribed in a circle.
Attention CAT Students!
To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.
|
Explore Courses for CAT exam
|
|
Top Courses for CATView all
There is an isosceles concyclic trapezium ABCD. AB II CD and AB > CD. AB = 10 cm. The perpendicular distance from the centre of the circle to AB is 5√3cm . What is the radius of the circle?a)10 cmb)10√3cmc)12√3cmd)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer?
Question Description
There is an isosceles concyclic trapezium ABCD. AB II CD and AB > CD. AB = 10 cm. The perpendicular distance from the centre of the circle to AB is 5√3cm . What is the radius of the circle?a)10 cmb)10√3cmc)12√3cmd)Cannot be determinedCorrect 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 There is an isosceles concyclic trapezium ABCD. AB II CD and AB > CD. AB = 10 cm. The perpendicular distance from the centre of the circle to AB is 5√3cm . What is the radius of the circle?a)10 cmb)10√3cmc)12√3cmd)Cannot be determinedCorrect 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 There is an isosceles concyclic trapezium ABCD. AB II CD and AB > CD. AB = 10 cm. The perpendicular distance from the centre of the circle to AB is 5√3cm . What is the radius of the circle?a)10 cmb)10√3cmc)12√3cmd)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer?.
There is an isosceles concyclic trapezium ABCD. AB II CD and AB > CD. AB = 10 cm. The perpendicular distance from the centre of the circle to AB is 5√3cm . What is the radius of the circle?a)10 cmb)10√3cmc)12√3cmd)Cannot be determinedCorrect 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 There is an isosceles concyclic trapezium ABCD. AB II CD and AB > CD. AB = 10 cm. The perpendicular distance from the centre of the circle to AB is 5√3cm . What is the radius of the circle?a)10 cmb)10√3cmc)12√3cmd)Cannot be determinedCorrect 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 There is an isosceles concyclic trapezium ABCD. AB II CD and AB > CD. AB = 10 cm. The perpendicular distance from the centre of the circle to AB is 5√3cm . What is the radius of the circle?a)10 cmb)10√3cmc)12√3cmd)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer?.
Solutions for There is an isosceles concyclic trapezium ABCD. AB II CD and AB > CD. AB = 10 cm. The perpendicular distance from the centre of the circle to AB is 5√3cm . What is the radius of the circle?a)10 cmb)10√3cmc)12√3cmd)Cannot be determinedCorrect 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 There is an isosceles concyclic trapezium ABCD. AB II CD and AB > CD. AB = 10 cm. The perpendicular distance from the centre of the circle to AB is 5√3cm . What is the radius of the circle?a)10 cmb)10√3cmc)12√3cmd)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
There is an isosceles concyclic trapezium ABCD. AB II CD and AB > CD. AB = 10 cm. The perpendicular distance from the centre of the circle to AB is 5√3cm . What is the radius of the circle?a)10 cmb)10√3cmc)12√3cmd)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for There is an isosceles concyclic trapezium ABCD. AB II CD and AB > CD. AB = 10 cm. The perpendicular distance from the centre of the circle to AB is 5√3cm . What is the radius of the circle?a)10 cmb)10√3cmc)12√3cmd)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of There is an isosceles concyclic trapezium ABCD. AB II CD and AB > CD. AB = 10 cm. The perpendicular distance from the centre of the circle to AB is 5√3cm . What is the radius of the circle?a)10 cmb)10√3cmc)12√3cmd)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice There is an isosceles concyclic trapezium ABCD. AB II CD and AB > CD. AB = 10 cm. The perpendicular distance from the centre of the circle to AB is 5√3cm . What is the radius of the circle?a)10 cmb)10√3cmc)12√3cmd)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup