Question

Construct ∆ PEN with PE = 4 cm, EN =5 cm and NP =3 cm. If you draw circles instead of arcs how many points of intersection do you get? How many triangles with given measurements are possible? Is this true in case of every triangle?

Answer 1

PE = 4cm,EN = 5cm, NP = 3crn. 

Step – 1: 

Draw a rough sketch of the triangle and label it with the given measurements. 

Step – 2: 

Draw a line segment EN of length 5 cm. 

Step – 3: 

With E as centre, draw on arc (circle) of radius 4 cm. 

Step – 4: 

With N as centre, draw another arc (circle) of radius 3 cm such that it intersects first arc at P. 

Step – 5: 

Join E, P and N, P. The required ∆PEN is constructed,

if we draw circles instead of arcs, we get two points of intersection. Then, we can draw two triangles with the given measurements. Yes, this is true in case of every triangle.

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