A Vector Ratio on a Secant

★ 7/10Power of a Point analytic geometry

Problem

Consider the circle $C:(x-2)^2+(y-2)^2=1$ . Through a point $A$ on the $x$ -axis, a line $l$ meets the circle $C$ at two points $M$ and $N$ with

\overrightarrow{AM}=2\overrightarrow{MN}.

Find the range of the $x$ -coordinate of $A$ .

Answer

Solution

Difficulty	7/10
Topics	Power of a Point, analytic geometry

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