The sides BC, CA and AB of a triangle ABC have 3, 4 and 5 interior points respectively on them. The number of triangles that can be constructed using these points as vertices is

Q. If the sides

A B

B C

and

C A

of a

△ A B C

have

a

b

and

c

points lying on them respectively, then the number of triangles that can be constructed using these points as vertices, if

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The sides AB,BC and CA of a △ABC have respectively 3,4 and 5 points lying on them. The number of triangles that can be constructed using these points as vertices is

The correct option is A 205There are 3+4+5=12 points in a plane.The number of required triangles= (The number of triangles formed by these 12 points) − (The number of triangles formed by the collinear points)=12C3−(3C3+4C3+5C3)=220−(1+4+10)=205

The sides $A B, B C$ and $C A$ of a $△ A B C$ have respectively $3, 4$ and $5$ points lying on them. The number of triangles that can be constructed using these points as vertices is