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3 problems match “circles”. Clear

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1. Minimum distance between points on circles ●○○○○ 10 ptsLet $z$ and $w$ be complex numbers such that $|z| = 2$ and $|w| = 5$. Find the smallest possible value of $|w - z|$.
2. Area of circle through three points ●●○○○ 20 ptsA circle passes through the points $(1,1)$, $(1,7)$, and $(9,1)$. The area of the circle can be expressed as $k\pi$. Find the value of $k$.
3. Angle at vertex of clock star polygon ●●○○○ 20 ptsA star polygon is drawn on a clock face by drawing a chord from each number to the fifth number clockwise from that number. That is, chords are drawn from 12 to 5, from 5 to 10, from 10 to 3, and so on, ending back at 12. Find the degree measure of the angle at each vertex of the star polygon.