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A triangle ABC is to be constructed with BC = 5 cm, angle B = 90° and AB + AC = 9 cm.
In the sum-of-sides construction, after marking D so that BD = 9 cm on the ray from B, what is the relationship between A and the segment DC?

Class 9Constructions of TrianglesGeometry
  • AA lies on the perpendicular bisector of DC
  • BA lies on the perpendicular bisector of BC
  • CA is the midpoint of BD
  • DA is the midpoint of DC

Step-by-Step Solution

The perpendicular bisector of DC meets BD at A, giving AD = AC. Then AB + AC = AB + AD = BD = 9 cm, satisfying the given sum.
Answer: A) A lies on the perpendicular bisector of DC

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