A 45-Degree Viewing Angle

★ 6/10Tangent Circle Circles analytic geometry

Problem

Consider the circle $C \colon x^2 + y^2 = 2$ and the line $l \colon x + 2y - 4 = 0$ , and let $P(x_0, y_0)$ be a point on $l$ . If there exists a point $Q$ on the circle $C$ such that $\angle OPQ = 45^\circ$ (where $O$ is the origin), find the range of possible values of $x_0$ .

Answer

Solution

Difficulty	6/10
Topics	Tangent Circle, Circles, analytic geometry

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