IOQM · Mathematics · Geometry
Chord-tangent properties, cyclic quadrilaterals, Ptolemy and power of a point.
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Q1 · Circles · HARD
Two circles with radii 5 and 12 are externally tangent to each other. A third circle is tangent to both circles and to their common external tangent. If this third circle lies between the two given circles, find its radius.
Q2 · Circles · HARD
Two circles of radii 5 and 12 are externally tangent to each other. A third circle is tangent to both and also tangent to their common external tangent line. Find the radius of the third circle.