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InterviewSolution
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Ăź) Write the method to determine the centre of a circle passing through three non-collinear points |
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Answer» The center of a circle passing through 3 non-collinear points is at the intersection of the perpendicular bisectors of the segments connecting those points. Sketch the figure of three such points, connect them with segments, and sketch each perpendicular bisector. Then sketch a segment from each point to the point of intersection of the bisectors. Using the SAS postulate you can prove the triangles formed by the bisector of one of these segments, half of the bisected segment and the segment you added are congruent triangles, and because corresponding parts are therefore congruent, and using the transitive property of congruence, you can prove the distances from the three points to the intersection point ate congruent. Thus that distance represents the radius of a circle connecting the three points. |
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