MATHEMATICS · Multi-part · GCSE · Mathematics · Geometry and Measures · Geometry and Measures
Problem
Triangle ABC has sides AB=6cm, BC=7cm and CA=5cm. A point P moves in the plane such that triangle PBC is congruent to triangle ABC.
(i) Describe step by step how you would construct every possible position of P.
(ii) Carry out the construction and clearly show the locus of P on your diagram.
(iii) How many distinct positions of P satisfy the given condition? Justify your answer with appropriate reasoning based on your construction.