Suppose BC is a given line segment in the plane and T is a scalene triangle. The number of points A in the plane such that the triangle with vertices A,B,C (in some order) is similar to triangle T is

Options

A. 4
B. 6
C. 12
D. 24

Answer

C

Explanation

Let triangle T is DEF possibilities

`therefore " A can take two positions if " triangleABC~triangleDEF`
`" We can arrange order of A,B,C in "3!=6 " ways"`
`" Total positions which A can take " =6xx2=12`