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Consider the following statements:
(1) The point of intersection of the perpendicular bisectors of the sides of a triangle may lie outside the triangle.
(2) The point of intersection of the perpendicular drawn from the vertices to the opposite side of a triangle may lie on two sides.
(1) The point of intersection of the perpendicular bisectors of the sides of a triangle may lie outside the triangle.
(2) The point of intersection of the perpendicular drawn from the vertices to the opposite side of a triangle may lie on two sides.
Q. Which of the above statements is/are correct?
- a)1 only
- b)2 only
- c)Both 1 and 2
- d)Neither 1 and 2
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Consider the following statements:(1)The point of intersection of the ...
Point of intersection of the perpendicular bisector is the circumcenter of the triangle.
It is possible for three chords to form a triangle but do not include the center when it is an obtuse angled triangle
∴ Statement 1 is possible
In a right triangle the perpendicular drawn from two vertices of the hypotenuse are the sides themselves. They meet on the vertex and lie on the side
∴ Statement 2 is possible
∴ Both 1 and 2 true
∴ Both 1 and 2 true
Most Upvoted Answer
Consider the following statements:(1)The point of intersection of the ...
Perpendicular Bisectors and Altitudes in a Triangle:
The first statement is correct. The point of intersection of the perpendicular bisectors of the sides of a triangle, known as the circumcenter, may indeed lie outside the triangle. This point is equidistant from the three vertices of the triangle and is the center of the circumcircle.
Perpendiculars from Vertices:
The second statement is also correct. The point of intersection of the perpendiculars drawn from the vertices to the opposite side of a triangle, known as the orthocenter, may lie on two sides of the triangle. This point is where the altitudes of the triangle meet.
Therefore, both statements are correct as they refer to different points of concurrency in a triangle - the circumcenter and the orthocenter. These points have specific properties and can lie both inside and outside the triangle based on the triangle's characteristics.
The first statement is correct. The point of intersection of the perpendicular bisectors of the sides of a triangle, known as the circumcenter, may indeed lie outside the triangle. This point is equidistant from the three vertices of the triangle and is the center of the circumcircle.
Perpendiculars from Vertices:
The second statement is also correct. The point of intersection of the perpendiculars drawn from the vertices to the opposite side of a triangle, known as the orthocenter, may lie on two sides of the triangle. This point is where the altitudes of the triangle meet.
Therefore, both statements are correct as they refer to different points of concurrency in a triangle - the circumcenter and the orthocenter. These points have specific properties and can lie both inside and outside the triangle based on the triangle's characteristics.
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Community Answer
Consider the following statements:(1)The point of intersection of the ...
Point of intersection of the perpendicular bisector is the circumcenter of the triangle.
It is possible for three chords to form a triangle but do not include the center when it is an obtuse angled triangle
∴ Statement 1 is possible
In a right triangle the perpendicular drawn from two vertices of the hypotenuse are the sides themselves. They meet on the vertex and lie on the side
∴ Statement 2 is possible
∴ Both 1 and 2 true
∴ Both 1 and 2 true
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Consider the following statements:(1)The point of intersection of the perpendicular bisectors of the sides of a triangle may lie outside the triangle.(2)The point of intersection of the perpendicular drawn from the vertices to the opposite side of a triangle may lie on two sides.Q. Which of the above statements is/are correct?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 and 2Correct answer is option 'C'. Can you explain this answer?
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Consider the following statements:(1)The point of intersection of the perpendicular bisectors of the sides of a triangle may lie outside the triangle.(2)The point of intersection of the perpendicular drawn from the vertices to the opposite side of a triangle may lie on two sides.Q. Which of the above statements is/are correct?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 and 2Correct answer is option 'C'. 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 Consider the following statements:(1)The point of intersection of the perpendicular bisectors of the sides of a triangle may lie outside the triangle.(2)The point of intersection of the perpendicular drawn from the vertices to the opposite side of a triangle may lie on two sides.Q. Which of the above statements is/are correct?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 and 2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following statements:(1)The point of intersection of the perpendicular bisectors of the sides of a triangle may lie outside the triangle.(2)The point of intersection of the perpendicular drawn from the vertices to the opposite side of a triangle may lie on two sides.Q. Which of the above statements is/are correct?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 and 2Correct answer is option 'C'. Can you explain this answer?.
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