Question

ABC is an isosceles triangle with AC = BC. If `A B^2=2A C^2`, prove that ABC is a right triangle.

Answer 1

Please refer to video for diagram of triangle.
Here, we are given,
`AC =BC`
and `AB^2 = 2AC^2`
`AB^2 = 2AC^2=>AB^2 = AC^2+AC^2`
As, `AC = BC`
`AB^2 = AC^2+BC^2->(1)`
For, a right angle triangle, we know,
`h^2=b^2+p^2`
If we consider AB as hypotenuse, AC and BC as base and perpendicular, then from (1), we can say that, `ABC` is a right angle triangle.