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Question

If A(3,4),B(3,2) and C(5,4), then which of the following statements is correct?

A
ABC forms a right angled triangle.
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B
ABC forms an acute angled triangle.
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C
ABC forms an obtuse angled triangle.
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D
ABC does not form a triangle.
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Solution

The correct option is C ABC forms an obtuse angled triangle.
Given : A(3,4),B(3,2),C(5,4)
AB=36+4=210 units
BC=4+36=210 units
AC=64+64=82 units
Checking the condition for formation of a triangle,
AB+BC>ACAB+AC>BCAC+BC>AB
So, it forms a triangle.

Now, AC2=128,AB2=40,BC2=40
AC2>AB2+BC2
Hence, ABC is an obtuse angled triangle.

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