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is isosceles with apex angle greater than or equal to 60°; and

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with equality if and only if the triangle is isosceles with apex angle less than or equal to 60°.

We also have

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and likewise for angles B, C, with equality in the first part if the triangle is isosceles and the apex angle is at least 60° and equality in the second part if and only if the triangle is isosceles with apex angle no greater than 60°.

Further, any two angle measures A and B opposite sides a and b respectively are

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