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Direction: Assertion
Statement 1: In triangle ABC, the centroid (G) divides the line joining orthocentre (O) and circumcentre (C) in ratio 2 : 1.
Reason
Statement 2: The centroid (G) divides the median AD in ratio 2 : 1. Select the correct
Statement 1: In triangle ABC, the centroid (G) divides the line joining orthocentre (O) and circumcentre (C) in ratio 2 : 1.
Reason
Statement 2: The centroid (G) divides the median AD in ratio 2 : 1. Select the correct
- a)Both the statements are TRUE and STATEMENT 2 is the correct expansion of STATEMENT 1
- b)Both the statements are TRUE but STATEMENT 2 is NOT the correct explanation of STATEMENT 1
- c)STATEMENT 1 is TRUE and STATEMENT 2 is FALSE
- d)STATEMENT 1 is FALSE and STATEMENT 2 is TRUE
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Direction: AssertionStatement 1: In triangle ABC, the centroid (G) div...
Assertion: In triangle ABC, the centroid (G) divides the line joining orthocentre (O) and circumcentre (C) in ratio 2:1.
Reason: The centroid (G) divides the median AD in ratio 2:1.
Explanation:
The centroid (G) of a triangle is the point of intersection of the medians of the triangle. A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side.
Statement 1: In triangle ABC, the centroid (G) divides the line joining orthocentre (O) and circumcentre (C) in ratio 2:1.
When the centroid divides a line segment joining two points, it divides it in the ratio of 2:1. This is true for any line segment joining two points and not specific to the orthocentre and circumcentre of a triangle. Hence, statement 1 is true.
Statement 2: The centroid (G) divides the median AD in ratio 2:1.
The centroid of a triangle divides each median in the ratio 2:1. This means that the distance from the vertex to the centroid is twice the distance from the centroid to the midpoint of the opposite side. Hence, statement 2 is true.
Conclusion:
Both statement 1 and statement 2 are true, but statement 2 is not the correct explanation of statement 1.
The ratio in statement 1 is true for any line segment joining two points, while statement 2 specifically refers to the centroid dividing a median in the ratio 2:1. Therefore, statement 2 does not provide an explanation for statement 1.
Hence, the correct answer is option B.
Reason: The centroid (G) divides the median AD in ratio 2:1.
Explanation:
The centroid (G) of a triangle is the point of intersection of the medians of the triangle. A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side.
Statement 1: In triangle ABC, the centroid (G) divides the line joining orthocentre (O) and circumcentre (C) in ratio 2:1.
When the centroid divides a line segment joining two points, it divides it in the ratio of 2:1. This is true for any line segment joining two points and not specific to the orthocentre and circumcentre of a triangle. Hence, statement 1 is true.
Statement 2: The centroid (G) divides the median AD in ratio 2:1.
The centroid of a triangle divides each median in the ratio 2:1. This means that the distance from the vertex to the centroid is twice the distance from the centroid to the midpoint of the opposite side. Hence, statement 2 is true.
Conclusion:
Both statement 1 and statement 2 are true, but statement 2 is not the correct explanation of statement 1.
The ratio in statement 1 is true for any line segment joining two points, while statement 2 specifically refers to the centroid dividing a median in the ratio 2:1. Therefore, statement 2 does not provide an explanation for statement 1.
Hence, the correct answer is option B.
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Community Answer
Direction: AssertionStatement 1: In triangle ABC, the centroid (G) div...
In the question, we have to check that the Statement 1: In triangle ABC, the centroid (G) divides the line joining orthocentre (O) and circumcentre (C) in ratio 2 : 1, is true or not and also we have to check that Statement 2: The centroid (G) divides the median AD in ratio 2 : 1, is correct or not. Finally, we have to check if statement 2 is the explanation of statement 1 or not.
So, here we know that In triangle ABC, the centroid (G) divides the line joining orthocentre (O) and circumcentre (C) in ratio 2 : 1. Also, we know that The centroid (G) divides the median AD in ratio 2 : 1. But the explanation given in statement 2 is not the correct reason for the statement 1 to be true.
So, from this we can say that option B, which says that Both the statements are TRUE but STATEMENT 2 is NOT the correct explanation of STATEMENT 1 is the correct answer.
Hence, option B is the correct answer.
So, here we know that In triangle ABC, the centroid (G) divides the line joining orthocentre (O) and circumcentre (C) in ratio 2 : 1. Also, we know that The centroid (G) divides the median AD in ratio 2 : 1. But the explanation given in statement 2 is not the correct reason for the statement 1 to be true.
So, from this we can say that option B, which says that Both the statements are TRUE but STATEMENT 2 is NOT the correct explanation of STATEMENT 1 is the correct answer.
Hence, option B is the correct answer.
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Direction: AssertionStatement 1: In triangle ABC, the centroid (G) divides the line joining orthocentre (O) and circumcentre (C) in ratio 2 : 1.ReasonStatement 2: The centroid (G) divides the median AD in ratio 2 : 1. Select the correcta)Both the statements are TRUE and STATEMENT 2 is the correct expansion of STATEMENT 1b)Both the statements are TRUE but STATEMENT 2 is NOT the correct explanation of STATEMENT 1c)STATEMENT 1 is TRUE and STATEMENT 2 is FALSEd)STATEMENT 1 is FALSE and STATEMENT 2 is TRUECorrect answer is option 'B'. Can you explain this answer?
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Direction: AssertionStatement 1: In triangle ABC, the centroid (G) divides the line joining orthocentre (O) and circumcentre (C) in ratio 2 : 1.ReasonStatement 2: The centroid (G) divides the median AD in ratio 2 : 1. Select the correcta)Both the statements are TRUE and STATEMENT 2 is the correct expansion of STATEMENT 1b)Both the statements are TRUE but STATEMENT 2 is NOT the correct explanation of STATEMENT 1c)STATEMENT 1 is TRUE and STATEMENT 2 is FALSEd)STATEMENT 1 is FALSE and STATEMENT 2 is TRUECorrect answer is option 'B'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Direction: AssertionStatement 1: In triangle ABC, the centroid (G) divides the line joining orthocentre (O) and circumcentre (C) in ratio 2 : 1.ReasonStatement 2: The centroid (G) divides the median AD in ratio 2 : 1. Select the correcta)Both the statements are TRUE and STATEMENT 2 is the correct expansion of STATEMENT 1b)Both the statements are TRUE but STATEMENT 2 is NOT the correct explanation of STATEMENT 1c)STATEMENT 1 is TRUE and STATEMENT 2 is FALSEd)STATEMENT 1 is FALSE and STATEMENT 2 is TRUECorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: AssertionStatement 1: In triangle ABC, the centroid (G) divides the line joining orthocentre (O) and circumcentre (C) in ratio 2 : 1.ReasonStatement 2: The centroid (G) divides the median AD in ratio 2 : 1. Select the correcta)Both the statements are TRUE and STATEMENT 2 is the correct expansion of STATEMENT 1b)Both the statements are TRUE but STATEMENT 2 is NOT the correct explanation of STATEMENT 1c)STATEMENT 1 is TRUE and STATEMENT 2 is FALSEd)STATEMENT 1 is FALSE and STATEMENT 2 is TRUECorrect answer is option 'B'. Can you explain this answer?.
Direction: AssertionStatement 1: In triangle ABC, the centroid (G) divides the line joining orthocentre (O) and circumcentre (C) in ratio 2 : 1.ReasonStatement 2: The centroid (G) divides the median AD in ratio 2 : 1. Select the correcta)Both the statements are TRUE and STATEMENT 2 is the correct expansion of STATEMENT 1b)Both the statements are TRUE but STATEMENT 2 is NOT the correct explanation of STATEMENT 1c)STATEMENT 1 is TRUE and STATEMENT 2 is FALSEd)STATEMENT 1 is FALSE and STATEMENT 2 is TRUECorrect answer is option 'B'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Direction: AssertionStatement 1: In triangle ABC, the centroid (G) divides the line joining orthocentre (O) and circumcentre (C) in ratio 2 : 1.ReasonStatement 2: The centroid (G) divides the median AD in ratio 2 : 1. Select the correcta)Both the statements are TRUE and STATEMENT 2 is the correct expansion of STATEMENT 1b)Both the statements are TRUE but STATEMENT 2 is NOT the correct explanation of STATEMENT 1c)STATEMENT 1 is TRUE and STATEMENT 2 is FALSEd)STATEMENT 1 is FALSE and STATEMENT 2 is TRUECorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: AssertionStatement 1: In triangle ABC, the centroid (G) divides the line joining orthocentre (O) and circumcentre (C) in ratio 2 : 1.ReasonStatement 2: The centroid (G) divides the median AD in ratio 2 : 1. Select the correcta)Both the statements are TRUE and STATEMENT 2 is the correct expansion of STATEMENT 1b)Both the statements are TRUE but STATEMENT 2 is NOT the correct explanation of STATEMENT 1c)STATEMENT 1 is TRUE and STATEMENT 2 is FALSEd)STATEMENT 1 is FALSE and STATEMENT 2 is TRUECorrect answer is option 'B'. Can you explain this answer?.
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Direction: AssertionStatement 1: In triangle ABC, the centroid (G) divides the line joining orthocentre (O) and circumcentre (C) in ratio 2 : 1.ReasonStatement 2: The centroid (G) divides the median AD in ratio 2 : 1. Select the correcta)Both the statements are TRUE and STATEMENT 2 is the correct expansion of STATEMENT 1b)Both the statements are TRUE but STATEMENT 2 is NOT the correct explanation of STATEMENT 1c)STATEMENT 1 is TRUE and STATEMENT 2 is FALSEd)STATEMENT 1 is FALSE and STATEMENT 2 is TRUECorrect answer is option 'B'. Can you explain this answer?, a detailed solution for Direction: AssertionStatement 1: In triangle ABC, the centroid (G) divides the line joining orthocentre (O) and circumcentre (C) in ratio 2 : 1.ReasonStatement 2: The centroid (G) divides the median AD in ratio 2 : 1. Select the correcta)Both the statements are TRUE and STATEMENT 2 is the correct expansion of STATEMENT 1b)Both the statements are TRUE but STATEMENT 2 is NOT the correct explanation of STATEMENT 1c)STATEMENT 1 is TRUE and STATEMENT 2 is FALSEd)STATEMENT 1 is FALSE and STATEMENT 2 is TRUECorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of Direction: AssertionStatement 1: In triangle ABC, the centroid (G) divides the line joining orthocentre (O) and circumcentre (C) in ratio 2 : 1.ReasonStatement 2: The centroid (G) divides the median AD in ratio 2 : 1. Select the correcta)Both the statements are TRUE and STATEMENT 2 is the correct expansion of STATEMENT 1b)Both the statements are TRUE but STATEMENT 2 is NOT the correct explanation of STATEMENT 1c)STATEMENT 1 is TRUE and STATEMENT 2 is FALSEd)STATEMENT 1 is FALSE and STATEMENT 2 is TRUECorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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