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When you construct the perpendicular bisector of side DC to locate vertex A (in the sum-of-sides construction), the key property used is that every point on it is:

Class 9Constructions of TrianglesGeometry
  • Aequidistant from D and C
  • Bequidistant from B and C
  • Con side BC
  • Dthe midpoint of BD

Step-by-Step Solution

A point on the perpendicular bisector of DC is equidistant from D and C. Choosing A on it gives AD = AC, which makes the side lengths come out correctly.
Answer: A) equidistant from D and C

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