Q3 of 28 Page 107

What will the locus of a point equidistant from three non-collinear points A, B and C? Explain the reason of your answer.

The locus of a point equidistant from three non-collinear points A, B and C is the circumcentre of the triangle.

The locus of the points is the point of intersection of the perpendicular bisectors of each of the two points. The circumcentre is equidistant from all the three points A, B and C.


Example:



Here in ∆RST, U is the circumcentre of the triangle and RC ,SB and TA are the perpendicular bisectors of sides ST, RT and RS.


More from this chapter

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1

Write true or false out of the following statements and give the justification of your answer.

(i) The set of points situated at equal distances from a line is a line.


(ii) A circle is the locus of those points which lie at a fixed distance from a given point.


(iii) Three given points will be collinear when they are not the members of the set of points of a line.


(iv) The locus of points equidistant from two lines will be a line parallel to both the lines.


(v) The locus of point equidistant from the given points is the perpendicular bisector of the line joining both the points.


 2

The diagonals of a quadrilateral bisect each other.

Prove that this quadrilateral as a parallelogram.


 4

What will be the locus of a point equidistant from three collinear points? Explain the reason of your answer.

 5

Prove that the locus of the centres of circles passing through points A and B is the perpendicular bisector of line segment AB.