Using ruler and compass construct: 1)a triangle ABC in which AB=5.5cm,BC=3.4cm and CA=4.9cm.? 2)locus of points equidistant from A and C.? 3)A circle touching AB at A and passing through C?

1 Answer
Jan 19, 2018

Drawn

Question (1)

Steps

  1. Three line segments of lengths 5.5 cm,3.4 cm and 4.9 cm are drawn using ruler .
  2. A line segment #AX>5.5# cm is drawn using ruler.
    Then #AB =5.5# cm is cut off from #AX# using compass.
  3. Centering B an arc of radius #3.4# cm is first drawn then another arc of radius #4.9# cm is also drawn centering A with the help of a compass. These two arcs intersect at C. #A,C and B,C# are joined. Thus required #Delta ABC# is obtained.

Question (2)

Steps

  1. The perpendicular bisector #(PQ)# of the side #AC# is drawn with the help of a ruler and a compass in usual way. This line PQ represents the locus of the point equidistant from #A and C#

Question (3)

Steps

  1. Perpendicular #AN# is drawn on AB at the point #A# using a ruler and a compass. Let #AN and PQ# intersect at #O#. This point #O# lying on the normal #AN# is also equidistant from #A and C#.
  2. A circle of radius #OA# centering #O# is drawn with the help of compass. This circle will pass through both #A and C#. Hence this circle is the required circle.