Let $$C_1$$ and $$C_2$$ be circles that intersect at right angles, having $$P_1$$ and $$P_2$$ as their centres. Then the circle with diameter $$\vec{P_1 P_2}$$ has a quarter of the area of the sum of the areas of $$C_1$$ and $$C_2$$.

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Proof: Pythagoras.

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@icecolbeveridge how do circles intersect at right angles?

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@christianp Like so. Maybe it's the tangents that do that, but I'd argue that it's fine in the limit.
mathstodon.xyz/media/IkoU5xjqj

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@christianp Take any two points on the circumference of a circle, draw the tangents at them, draw a circle with the tangent intersection as its centre. Well-known construction for some examples of hyperbolic geometries.

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