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Can someone please explain how the boundary points on a circle are also extreme points?

If i take a point inside the circle and one point on the boundary, I can take a convex combination of those two to get a third point on the boundary?

Rodrigo de Azevedo
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Mushahid Khan
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    The line segment connecting the two points (one in the circle, one on the boundary) only touches the boundary at one point (the endpoint on the boundary). Can you illustrate why you believe this segment touches the boundary at another point? – angryavian Jun 22 '23 at 04:11
  • A convex combination of $x$ and $y$ is strictly on the line segment connecting $x$ and $y$. It does not extend past the point on the interior of the circle so it never reaches the far side. – CyclotomicField Jun 26 '23 at 11:38

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