JEE Exam > JEE Questions > AB is a diameter of a circle and C is any poi...
Start Learning for Free
AB is a diameter of a circle and C is any point on the circumference of the circle. Then
- a)the area of D ABC is maximum when it is isosceles
- b)the area of D ABC is minimum when it is isosceles
- c)the perimeter of D ABC is minimum when it is isosceles
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
AB is a diameter of a circle and C is any point on the circumference o...
Yes A is correct coz suppose O be the centre of circle. When the triangle ABC is isosceles then CO will be the radius of the the circle and also the altitude and the base is diameter. These 2 are maximum in case of the triangle inscribed in a semicircle. so area will be maximum.
Free Test
| FREE | Start Free Test |
Community Answer
AB is a diameter of a circle and C is any point on the circumference o...
Analysis:
Let's analyze each option one by one.
a) The area of triangle ABC is maximum when it is isosceles.
To prove this, let's consider the triangle ABC as shown below:
A
/ \
C------B
Since AB is a diameter of the circle, angle ACB is a right angle. Let's consider angle CAB (angle A) and angle ABC (angle B) to be x.
Since the sum of angles in a triangle is 180 degrees, we have:
x + x + 90 = 180
2x = 90
x = 45
Now, let's draw the altitude from point C to the base AB and call it CD. Since triangle ABC is isosceles, the altitude will bisect the base AB. Let's call the point of intersection of CD and AB as E.
A
/ | \
C--D--B
|
E
Since CD bisects AB, CE = ED. Let's consider CE = ED = h.
Now, let's calculate the area of triangle ABC.
Area of triangle ABC = (1/2) * AB * CD
= (1/2) * AB * h
Since AB is fixed (as it is the diameter of the circle), the area of triangle ABC is directly proportional to the height h. And since CE = ED, the height h is maximum when triangle ABC is isosceles.
Therefore, the area of triangle ABC is maximum when it is isosceles. Hence, option a) is correct.
b) The area of triangle ABC is minimum when it is isosceles.
This statement is incorrect as we have just proved in option a) that the area of triangle ABC is maximum when it is isosceles.
c) The perimeter of triangle ABC is minimum when it is isosceles.
This statement is not mentioned in the question, so we cannot conclude anything about the perimeter of triangle ABC.
d) None of these.
Since option a) is correct, option d) is incorrect.
Hence, the correct answer is option a) - the area of triangle ABC is maximum when it is isosceles.
Let's analyze each option one by one.
a) The area of triangle ABC is maximum when it is isosceles.
To prove this, let's consider the triangle ABC as shown below:
A
/ \
C------B
Since AB is a diameter of the circle, angle ACB is a right angle. Let's consider angle CAB (angle A) and angle ABC (angle B) to be x.
Since the sum of angles in a triangle is 180 degrees, we have:
x + x + 90 = 180
2x = 90
x = 45
Now, let's draw the altitude from point C to the base AB and call it CD. Since triangle ABC is isosceles, the altitude will bisect the base AB. Let's call the point of intersection of CD and AB as E.
A
/ | \
C--D--B
|
E
Since CD bisects AB, CE = ED. Let's consider CE = ED = h.
Now, let's calculate the area of triangle ABC.
Area of triangle ABC = (1/2) * AB * CD
= (1/2) * AB * h
Since AB is fixed (as it is the diameter of the circle), the area of triangle ABC is directly proportional to the height h. And since CE = ED, the height h is maximum when triangle ABC is isosceles.
Therefore, the area of triangle ABC is maximum when it is isosceles. Hence, option a) is correct.
b) The area of triangle ABC is minimum when it is isosceles.
This statement is incorrect as we have just proved in option a) that the area of triangle ABC is maximum when it is isosceles.
c) The perimeter of triangle ABC is minimum when it is isosceles.
This statement is not mentioned in the question, so we cannot conclude anything about the perimeter of triangle ABC.
d) None of these.
Since option a) is correct, option d) is incorrect.
Hence, the correct answer is option a) - the area of triangle ABC is maximum when it is isosceles.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
AB is a diameter of a circle and C is any point on the circumference of the circle. Thena)the area of D ABC is maximum when it is isoscelesb)the area of D ABC is minimum when it is isoscelesc)the perimeter of D ABC is minimum when it is isoscelesd)none of theseCorrect answer is option 'A'. Can you explain this answer?
Question Description
AB is a diameter of a circle and C is any point on the circumference of the circle. Thena)the area of D ABC is maximum when it is isoscelesb)the area of D ABC is minimum when it is isoscelesc)the perimeter of D ABC is minimum when it is isoscelesd)none of theseCorrect answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about AB is a diameter of a circle and C is any point on the circumference of the circle. Thena)the area of D ABC is maximum when it is isoscelesb)the area of D ABC is minimum when it is isoscelesc)the perimeter of D ABC is minimum when it is isoscelesd)none of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for AB is a diameter of a circle and C is any point on the circumference of the circle. Thena)the area of D ABC is maximum when it is isoscelesb)the area of D ABC is minimum when it is isoscelesc)the perimeter of D ABC is minimum when it is isoscelesd)none of theseCorrect answer is option 'A'. Can you explain this answer?.
AB is a diameter of a circle and C is any point on the circumference of the circle. Thena)the area of D ABC is maximum when it is isoscelesb)the area of D ABC is minimum when it is isoscelesc)the perimeter of D ABC is minimum when it is isoscelesd)none of theseCorrect answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about AB is a diameter of a circle and C is any point on the circumference of the circle. Thena)the area of D ABC is maximum when it is isoscelesb)the area of D ABC is minimum when it is isoscelesc)the perimeter of D ABC is minimum when it is isoscelesd)none of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for AB is a diameter of a circle and C is any point on the circumference of the circle. Thena)the area of D ABC is maximum when it is isoscelesb)the area of D ABC is minimum when it is isoscelesc)the perimeter of D ABC is minimum when it is isoscelesd)none of theseCorrect answer is option 'A'. Can you explain this answer?.
Solutions for AB is a diameter of a circle and C is any point on the circumference of the circle. Thena)the area of D ABC is maximum when it is isoscelesb)the area of D ABC is minimum when it is isoscelesc)the perimeter of D ABC is minimum when it is isoscelesd)none of theseCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of AB is a diameter of a circle and C is any point on the circumference of the circle. Thena)the area of D ABC is maximum when it is isoscelesb)the area of D ABC is minimum when it is isoscelesc)the perimeter of D ABC is minimum when it is isoscelesd)none of theseCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
AB is a diameter of a circle and C is any point on the circumference of the circle. Thena)the area of D ABC is maximum when it is isoscelesb)the area of D ABC is minimum when it is isoscelesc)the perimeter of D ABC is minimum when it is isoscelesd)none of theseCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for AB is a diameter of a circle and C is any point on the circumference of the circle. Thena)the area of D ABC is maximum when it is isoscelesb)the area of D ABC is minimum when it is isoscelesc)the perimeter of D ABC is minimum when it is isoscelesd)none of theseCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of AB is a diameter of a circle and C is any point on the circumference of the circle. Thena)the area of D ABC is maximum when it is isoscelesb)the area of D ABC is minimum when it is isoscelesc)the perimeter of D ABC is minimum when it is isoscelesd)none of theseCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice AB is a diameter of a circle and C is any point on the circumference of the circle. Thena)the area of D ABC is maximum when it is isoscelesb)the area of D ABC is minimum when it is isoscelesc)the perimeter of D ABC is minimum when it is isoscelesd)none of theseCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE 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