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Three distinct lines are drawn in a plane. Suppose there exactly exist n circle in the plane tangent to all the three lines then the possible values of n are ? Plz Explain a)0 b)1 c)2 d)4?
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Three distinct lines are drawn in a plane. Suppose there exactly exist...
Solution:
Case 1: When the three lines meet at a point
In this case, there is only one circle that can be drawn which is tangent to all three lines, and that is the circle with the point of intersection as its center.
Therefore, the possible value of n is 1.
Case 2: When the three lines are parallel
In this case, no circle can be drawn which is tangent to all three lines, as the distance between the parallel lines remains constant and a circle cannot be tangent to them.
Therefore, the possible value of n is 0.
Case 3: When the three lines are neither parallel nor concurrent
In this case, we can draw two circles which are tangent to all three lines. The centers of these circles lie on the line which is perpendicular to the three given lines and passes through their intersection point.
Therefore, the possible value of n is 2.
Case 4: When two lines are parallel and the third is not
In this case, we can draw four circles which are tangent to all three lines. Two of these circles have their centers on the line which is perpendicular to the parallel lines and passes through their point of intersection, while the other two circles have their centers on the line which is parallel to the two parallel lines and passes through the intersection point of the third line with the line joining the centers of the two circles on the perpendicular line.
Therefore, the possible value of n is 4.
Hence, the possible values of n are 0, 1, 2, and 4.
Case 1: When the three lines meet at a point
In this case, there is only one circle that can be drawn which is tangent to all three lines, and that is the circle with the point of intersection as its center.
Therefore, the possible value of n is 1.
Case 2: When the three lines are parallel
In this case, no circle can be drawn which is tangent to all three lines, as the distance between the parallel lines remains constant and a circle cannot be tangent to them.
Therefore, the possible value of n is 0.
Case 3: When the three lines are neither parallel nor concurrent
In this case, we can draw two circles which are tangent to all three lines. The centers of these circles lie on the line which is perpendicular to the three given lines and passes through their intersection point.
Therefore, the possible value of n is 2.
Case 4: When two lines are parallel and the third is not
In this case, we can draw four circles which are tangent to all three lines. Two of these circles have their centers on the line which is perpendicular to the parallel lines and passes through their point of intersection, while the other two circles have their centers on the line which is parallel to the two parallel lines and passes through the intersection point of the third line with the line joining the centers of the two circles on the perpendicular line.
Therefore, the possible value of n is 4.
Hence, the possible values of n are 0, 1, 2, and 4.
Community Answer
Three distinct lines are drawn in a plane. Suppose there exactly exist...
C if those 3 lines form a triangle then 4 circles r formed (incircle n 3 excircles) .If those 3 lines r concur or parallel then 0 circles r formed .N if 2 r parallel n the 3rd one is not then 2 circles r formed.hence,(2,4,0 ) r correct options.
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Three distinct lines are drawn in a plane. Suppose there exactly exist n circle in the plane tangent to all the three lines then the possible values of n are ? Plz Explain a)0 b)1 c)2 d)4?
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Three distinct lines are drawn in a plane. Suppose there exactly exist n circle in the plane tangent to all the three lines then the possible values of n are ? Plz Explain a)0 b)1 c)2 d)4? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Three distinct lines are drawn in a plane. Suppose there exactly exist n circle in the plane tangent to all the three lines then the possible values of n are ? Plz Explain a)0 b)1 c)2 d)4? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three distinct lines are drawn in a plane. Suppose there exactly exist n circle in the plane tangent to all the three lines then the possible values of n are ? Plz Explain a)0 b)1 c)2 d)4?.
Three distinct lines are drawn in a plane. Suppose there exactly exist n circle in the plane tangent to all the three lines then the possible values of n are ? Plz Explain a)0 b)1 c)2 d)4? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Three distinct lines are drawn in a plane. Suppose there exactly exist n circle in the plane tangent to all the three lines then the possible values of n are ? Plz Explain a)0 b)1 c)2 d)4? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three distinct lines are drawn in a plane. Suppose there exactly exist n circle in the plane tangent to all the three lines then the possible values of n are ? Plz Explain a)0 b)1 c)2 d)4?.
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