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Question
ABC is a triangle. Number of circles that can be drawn circumscribing the triangle is/are ?
ABC is a triangle. Number of circles that can be drawn circumscribing the triangle is/are ?
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Solution
The correct option is A 1
For the triangle ABC let us draw perpendicular bisectors for AB and AC. Let the point of intersection of these two lines be O. since we know that any point on the perpendicular bisector of a line segment is equidistant from the end points OA=OB and OB=O,Thus OA=OB=OC.Now if we draw a circle with O as center and OA as radius it will pass through points B and C. since two lines can intersect at only one point only one circle can be drawn circumscribing the triangle.
For the triangle ABC let us draw perpendicular bisectors for AB and AC. Let the point of intersection of these two lines be O. since we know that any point on the perpendicular bisector of a line segment is equidistant from the end points OA=OB and OB=O,Thus OA=OB=OC.Now if we draw a circle with O as center and OA as radius it will pass through points B and C. since two lines can intersect at only one point only one circle can be drawn circumscribing the triangle.
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