diameter = hypotenuse =h
h^2 = 6^2+8^2 = 36+64=100
h=10

I have a doubt here. The question says that two legs are 6 and 8. How can we be sure that 8 is not the longest side(i.e the diameter)?

Good question my friend !!

There are however two things to note.
1.The triangle is a right triangle
2.The triangle is inscribed in a circle .

and I believe inscribed means a geometrical shape which would fit (properly with all the vertices touching the circle) inside the other,
and if the shape, which is this case is a triangle fits , it must have all 3 vertices touching the circle ,also since it is a right triangle the diameter will subtend 90 degree angle on the circle.
Hence 8 cannot be the diameter.

Good question.
In a right triangle, the longest side is called the hypotenuse, and the other two (shorter) sides (that create the right angle) are called legs.

Cheers,
Brent
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