A locus of points which is equidistant from three non-collinear points is the ___ centre of the circle through the given points.

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Solution

A locus of points which is equidistant from three non-collinear points is the circumcentre of the circle through the given points.

Proof:-

Let A, B and C be any three non-collinear points. Join AB and BC. Then draw the perpendicular bisectors for AB and BC.

Consider their meeting point to be point O. Here, OA=OB=OC

$\Rightarrow$ O is equidistant from A, B and C and its the circumcentre of the circle passing through these points.

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Similar questions

A, B

C

Describe:

(i) The locus of points at distances less than 3 cm from a given point.

(ii) The locus of points at distances greater than 4 cm from a given point.

(iii) The locus of points at distances less than 2.5 cm from a given point.

(iv) The locus of points at distances greater than or equal to 35 mm cm from a given point.

(v) The locus of the centre of a given circle which rolls around the outside of a second circle and is always touching it.

(vi) The locus of the centres of all circles that are tangent to both the arms of a given angle.

(vii) The locus of the mid-points of all chords parallel to a given chord of a circle.

(viii) The locus of points within a circle that are equidistant from the end points of a given chord.

Given three non - collinear points, only one circle can be drawn through these three points.

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