Question

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?

Answer 1

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.