For questions about geometric shapes, congruences, similarities, transformations, as well as the properties of classes of figures, points, lines, angles.

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A trigonometric problem when calculating distance to the boundary of a convex hull

Suppose we have a sphere and a point outside of the sphere. We denote the point outside as $v$ and the origin of the sphere as $x$. The convex hull of the sphere and $v$ should be like an ice cream ...
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solve this 1999 problem with geometry

if $\bigodot P\bigcap \bigodot Q=A,B$,and the common tangent is $C,D$,and $E\in BA$,and $EC\bigcap \bigodot P=F,ED\bigcap \bigodot Q=G$,and if $\angle FAH=\angle HAG$ show that $$\angle FCH=\...