Definition:Right Circular Cone/Obtuse-Angled

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Let $K$ be a right circular cone.

Then $K$ is obtuse-angled if and only if the opening angle of $K$ is an obtuse angle.

In the words of Euclid:

When, one side of those about the right angle in a right-angled triangle remaining fixed, the triangle is carried round and restored again to the same position from which it began to be moved, the figure so comprehended is a cone.
And, if the straight line which remains fixed be equal to the remaining side about the right angle which is carried round, the cone will be right-angled; if less, obtuse-angled; and if greater, acute-angled.

(The Elements: Book $\text{XI}$: Definition $18$)