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Construct triangle ABC, with AB = 7 cm, BC = 8 cm and ∠ABC = 60°. Locate by construction the point P such that :

(i) P is equidistant from B and C and

(ii) P is equidistant from AB and BC.

(iii) Measure and record the length of PB.

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Answer

Construct the △ABC with the given data:

Construct triangle ABC, with AB = 7 cm, BC = 8 cm and ∠ABC = 60°. Locate by construction the point P such that (i) P is equidistant from B and C and (ii) P is equidistant from AB and BC. (iii) Measure and record the length of PB. Locus, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

(i) Since, P is equidistant from B and C hence, it will be a point on the perpendicular bisector of BC i.e. YZ.

(ii) Since, P is also equidistant from AB and BC, so, it will be a point on angle bisector of B i.e. BX.

Hence, the intersection of BX and YZ is point P.

(iii) The length of PB is 4.6 cm.

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