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Let ABC be a triangle in which AB = AC. Let L be the locus of points X inside or on the triangle such that BX = CX. Which of the following statements are correct?
(1) L is a straight line passing through A and in-centre of triangle ABC is on L.
(2) L is a straight line passing through A and orthocentre of triangle ABC is on L.
(3) L is a straight line passing through A and centroid of triangle ABC is on L.
Select the correct answer using the code given below. 
  • a)
    1 and 2 only
  • b)
    2 and 3 only
  • c)
    1 and 3 only
  • d)
    1, 2 and 3
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Let ABC be a triangle in which AB = AC. Let L be the locus of points X...

In triangle ABX and ACX
AB = AC [Given]
AX is common
BX = CX [Condition given]
⇒ ABX ≅ ACX [SSS ≅]
⇒ ∠BAX = ∠CAX
⇒ Locus of the points X such that BX = CX is the angle bisector of the ∠BAC
The line passes through in-centre because in-centre is the point of intersection of angle bisectors
In isosceles triangle, Orthocentre and centroid coincides with in-centre
∴ All three statements are true
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Most Upvoted Answer
Let ABC be a triangle in which AB = AC. Let L be the locus of points X...
Explanation:

Given:
- Triangle ABC with AB = AC
- Locus of points X inside or on the triangle such that BX = CX

Statement analysis:
- (1) L is a straight line passing through A and in-centre of triangle ABC is on L.
- (2) L is a straight line passing through A and orthocentre of triangle ABC is on L.
- (3) L is a straight line passing through A and centroid of triangle ABC is on L.

Analysis of each statement:
- (1) In-centre of a triangle is equidistant from all three sides. Since BX = CX, the locus of points equidistant from two points is the perpendicular bisector of the segment joining those two points. Therefore, L will be a straight line passing through A and in-centre of triangle ABC will lie on L.
- (2) Orthocentre is the point of concurrence of the altitudes of a triangle. Since BX = CX, the locus of points equidistant from two points is the perpendicular bisector of the segment joining those two points. Therefore, L will be a straight line passing through A, but the orthocentre may or may not lie on L.
- (3) Centroid is the point of concurrence of medians of a triangle. Since BX = CX, the locus of points equidistant from two points is the perpendicular bisector of the segment joining those two points. Therefore, L will be a straight line passing through A and centroid of triangle ABC will lie on L.
Therefore, all three statements are correct and the correct answer is option 'D'.
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Let ABC be a triangle in which AB = AC. Let L be the locus of points X inside or on the triangle such that BX = CX. Which of the following statements are correct?(1) L is a straight line passing through A and in-centre of triangle ABC is on L.(2) L is a straight line passing through A and orthocentre of triangle ABC is on L.(3) L is a straight line passing through A and centroid of triangle ABC is on L.Select the correct answer using the code given below.a)1 and 2 onlyb)2 and 3 onlyc)1 and 3 onlyd)1, 2 and 3Correct answer is option 'D'. Can you explain this answer?
Question Description
Let ABC be a triangle in which AB = AC. Let L be the locus of points X inside or on the triangle such that BX = CX. Which of the following statements are correct?(1) L is a straight line passing through A and in-centre of triangle ABC is on L.(2) L is a straight line passing through A and orthocentre of triangle ABC is on L.(3) L is a straight line passing through A and centroid of triangle ABC is on L.Select the correct answer using the code given below.a)1 and 2 onlyb)2 and 3 onlyc)1 and 3 onlyd)1, 2 and 3Correct answer is option 'D'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Let ABC be a triangle in which AB = AC. Let L be the locus of points X inside or on the triangle such that BX = CX. Which of the following statements are correct?(1) L is a straight line passing through A and in-centre of triangle ABC is on L.(2) L is a straight line passing through A and orthocentre of triangle ABC is on L.(3) L is a straight line passing through A and centroid of triangle ABC is on L.Select the correct answer using the code given below.a)1 and 2 onlyb)2 and 3 onlyc)1 and 3 onlyd)1, 2 and 3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let ABC be a triangle in which AB = AC. Let L be the locus of points X inside or on the triangle such that BX = CX. Which of the following statements are correct?(1) L is a straight line passing through A and in-centre of triangle ABC is on L.(2) L is a straight line passing through A and orthocentre of triangle ABC is on L.(3) L is a straight line passing through A and centroid of triangle ABC is on L.Select the correct answer using the code given below.a)1 and 2 onlyb)2 and 3 onlyc)1 and 3 onlyd)1, 2 and 3Correct answer is option 'D'. Can you explain this answer?.
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