CAT Exam > CAT Questions > DIRECTIONS for the question:Solve the followi...
Start Learning for Free
DIRECTIONS for the question: Solve the following question and mark the best possible option.
Two circles intersect each other at C and D. Line AB is their common tangent. What is the sum of measures of ∠ACB and ∠ADB?
- a)180°
- b)90°
- c)270°
- d)Indeterminate
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
DIRECTIONS for the question:Solve the following question and mark the ...
∠BAC = ∠ADC (as both intercept same arc)
∠ABC = 1/2m (arc BC) = ∠BDC
∴ ∠BAC + ∠ABC = ∠ADC + ∠BDC
Add ∠ACB to both sides,
∠BAC + ∠ABC + ∠ACB
=∠ADC + ∠BDC +∠ACB
∴ ∠ADB + ∠ACB = 1800
[
the sum of all angles of a triangle = 1800].
∠ABC = 1/2m (arc BC) = ∠BDC
∴ ∠BAC + ∠ABC = ∠ADC + ∠BDC
Add ∠ACB to both sides,
∠BAC + ∠ABC + ∠ACB
=∠ADC + ∠BDC +∠ACB
∴ ∠ADB + ∠ACB = 1800
[
the sum of all angles of a triangle = 1800].Hence, [1]
Most Upvoted Answer
DIRECTIONS for the question:Solve the following question and mark the ...
Explanation:
- Two circles intersect each other at C and D. Line AB is their common tangent.
- Let's denote the center of the first circle as O1, the center of the second circle as O2, point C as the point of intersection of the circles, and point D as the other point of intersection.
- Since line AB is the common tangent to both circles, it is perpendicular to the line joining the centers O1 and O2 at the point of contact.
- This means that triangle ACO1 and triangle ADO2 are right-angled triangles.
- Therefore, ∠ACO1 = 90° and ∠ADO2 = 90°.
- The sum of the measures of ∠ACB and ∠ADB will be equal to the sum of the measures of ∠ACO1 and ∠ADO2, which is 90° + 90° = 180°.
- Hence, the correct answer is option 'A' - 180°.
- Two circles intersect each other at C and D. Line AB is their common tangent.
- Let's denote the center of the first circle as O1, the center of the second circle as O2, point C as the point of intersection of the circles, and point D as the other point of intersection.
- Since line AB is the common tangent to both circles, it is perpendicular to the line joining the centers O1 and O2 at the point of contact.
- This means that triangle ACO1 and triangle ADO2 are right-angled triangles.
- Therefore, ∠ACO1 = 90° and ∠ADO2 = 90°.
- The sum of the measures of ∠ACB and ∠ADB will be equal to the sum of the measures of ∠ACO1 and ∠ADO2, which is 90° + 90° = 180°.
- Hence, the correct answer is option 'A' - 180°.
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
DIRECTIONS for the question:Solve the following question and mark the best possible option.Two circles intersect each other at C and D. Line AB is their common tangent. What is the sum of measures of ∠ACB and ∠ADB?a)180°b)90°c)270°d)IndeterminateCorrect answer is option 'A'. Can you explain this answer?
Question Description
DIRECTIONS for the question:Solve the following question and mark the best possible option.Two circles intersect each other at C and D. Line AB is their common tangent. What is the sum of measures of ∠ACB and ∠ADB?a)180°b)90°c)270°d)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 DIRECTIONS for the question:Solve the following question and mark the best possible option.Two circles intersect each other at C and D. Line AB is their common tangent. What is the sum of measures of ∠ACB and ∠ADB?a)180°b)90°c)270°d)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 DIRECTIONS for the question:Solve the following question and mark the best possible option.Two circles intersect each other at C and D. Line AB is their common tangent. What is the sum of measures of ∠ACB and ∠ADB?a)180°b)90°c)270°d)IndeterminateCorrect answer is option 'A'. Can you explain this answer?.
DIRECTIONS for the question:Solve the following question and mark the best possible option.Two circles intersect each other at C and D. Line AB is their common tangent. What is the sum of measures of ∠ACB and ∠ADB?a)180°b)90°c)270°d)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 DIRECTIONS for the question:Solve the following question and mark the best possible option.Two circles intersect each other at C and D. Line AB is their common tangent. What is the sum of measures of ∠ACB and ∠ADB?a)180°b)90°c)270°d)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 DIRECTIONS for the question:Solve the following question and mark the best possible option.Two circles intersect each other at C and D. Line AB is their common tangent. What is the sum of measures of ∠ACB and ∠ADB?a)180°b)90°c)270°d)IndeterminateCorrect answer is option 'A'. Can you explain this answer?.
Solutions for DIRECTIONS for the question:Solve the following question and mark the best possible option.Two circles intersect each other at C and D. Line AB is their common tangent. What is the sum of measures of ∠ACB and ∠ADB?a)180°b)90°c)270°d)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 DIRECTIONS for the question:Solve the following question and mark the best possible option.Two circles intersect each other at C and D. Line AB is their common tangent. What is the sum of measures of ∠ACB and ∠ADB?a)180°b)90°c)270°d)IndeterminateCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
DIRECTIONS for the question:Solve the following question and mark the best possible option.Two circles intersect each other at C and D. Line AB is their common tangent. What is the sum of measures of ∠ACB and ∠ADB?a)180°b)90°c)270°d)IndeterminateCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for DIRECTIONS for the question:Solve the following question and mark the best possible option.Two circles intersect each other at C and D. Line AB is their common tangent. What is the sum of measures of ∠ACB and ∠ADB?a)180°b)90°c)270°d)IndeterminateCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of DIRECTIONS for the question:Solve the following question and mark the best possible option.Two circles intersect each other at C and D. Line AB is their common tangent. What is the sum of measures of ∠ACB and ∠ADB?a)180°b)90°c)270°d)IndeterminateCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice DIRECTIONS for the question:Solve the following question and mark the best possible option.Two circles intersect each other at C and D. Line AB is their common tangent. What is the sum of measures of ∠ACB and ∠ADB?a)180°b)90°c)270°d)IndeterminateCorrect 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