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Draw two intersecting lines to include an angle of 30°. Use ruler and compasses to locate points which are equidistant from these lines and also 2 cm away from their point of intersection. How many such point exist ?

Locus

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Answer

Let two intersecting lines be AB and CD making angles of 30° and 150°. Let these lines intersect at O.

Draw two intersecting lines to include an angle of 30°. Use ruler and compasses to locate points which are equidistant from these lines and also 2 cm away from their point of intersection. How many such point exist ? Locus, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

We know that locus of points equidistant from two lines is the angle bisector of angle between them.

From figure,

EF and GH are angular bisectors of AB and CD.

Construct a circle taking O as centre and radius as 2 cm. This circle meet the bisectors at four points P, Q, R and S.

Hence, there are 4 points that are equidistant from two intersecting lines and 2 cm away from their point of intersection.

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