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The radius of the circumcircle of the triangle made by x-axis, y-axis and 4x + 3y = 12 is (SSC CGL 2nd Sit. 2012)
- a)2 unit
- b)2.5 unit
- c)3 unit
- d)4 unit
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The radius of the circumcircle of the triangle made by x-axis, y-axis ...
Putting x = 0 in 4x + 3y = 12 we get y = 4
Putting y = 0 in 4x + 3y = 12 we get x = 3
The triangle so formed is right angle triangle with points (0, 0), (3, 0) and (0, 4)
So diameter is the hypotenus of triangle
= 5 unit
Radius = 2.5 unit
Putting y = 0 in 4x + 3y = 12 we get x = 3
The triangle so formed is right angle triangle with points (0, 0), (3, 0) and (0, 4)
So diameter is the hypotenus of triangle
= 5 unit
Radius = 2.5 unit
Most Upvoted Answer
The radius of the circumcircle of the triangle made by x-axis, y-axis ...
Equation of the Triangle:
The equation of the given triangle is 4x + 3y = 12, where x and y intercepts are 3 and 4 respectively.
Coordinates of the Vertices:
The vertices of the triangle are at (0,0), (3,0), and (0,4) where the triangle meets the x-axis, y-axis, and the given line.
Center of the Circumcircle:
The center of the circumcircle of a triangle is the point of intersection of the perpendicular bisectors of its sides. Since the triangle is right-angled and isosceles, the circumcenter lies at the midpoint of the hypotenuse.
Midpoint of the Hypotenuse:
The midpoint of the hypotenuse of the triangle is calculated as ((3+0)/2, (0+4)/2) = (1.5, 2).
Radius of the Circumcircle:
The distance between the circumcenter and any of the vertices of the triangle is the radius of the circumcircle. Using the distance formula, we get the radius as sqrt((1.5-0)^2 + (2-0)^2) = sqrt(2.25 + 4) = sqrt(6.25) = 2.5 units.
Therefore, the radius of the circumcircle of the triangle formed by the x-axis, y-axis, and the line 4x + 3y = 12 is 2.5 units, which corresponds to option B.
The equation of the given triangle is 4x + 3y = 12, where x and y intercepts are 3 and 4 respectively.
Coordinates of the Vertices:
The vertices of the triangle are at (0,0), (3,0), and (0,4) where the triangle meets the x-axis, y-axis, and the given line.
Center of the Circumcircle:
The center of the circumcircle of a triangle is the point of intersection of the perpendicular bisectors of its sides. Since the triangle is right-angled and isosceles, the circumcenter lies at the midpoint of the hypotenuse.
Midpoint of the Hypotenuse:
The midpoint of the hypotenuse of the triangle is calculated as ((3+0)/2, (0+4)/2) = (1.5, 2).
Radius of the Circumcircle:
The distance between the circumcenter and any of the vertices of the triangle is the radius of the circumcircle. Using the distance formula, we get the radius as sqrt((1.5-0)^2 + (2-0)^2) = sqrt(2.25 + 4) = sqrt(6.25) = 2.5 units.
Therefore, the radius of the circumcircle of the triangle formed by the x-axis, y-axis, and the line 4x + 3y = 12 is 2.5 units, which corresponds to option B.
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The radius of the circumcircle of the triangle made by x-axis, y-axis and 4x + 3y = 12 is (SSC CGL 2nd Sit. 2012)a)2 unitb)2.5 unitc)3 unitd)4 unitCorrect answer is option 'B'. Can you explain this answer?
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