Midpoints of Tangent Chords

★ 7/10Pole and Polar Circles Power of a Point analytic geometry

Problem

From an arbitrary point $P$ of the line $l \colon x + y = 2$ , two tangent lines are drawn to the circle $C \colon x^2 + y^2 = 1$ , touching it at $A$ and $B$ . Let $Q$ be the midpoint of segment $AB$ . Find the range of possible distances from $Q$ to the line $l$ .

Answer

Solution

Difficulty	7/10
Topics	Pole and Polar, Circles, Power of a Point, analytic geometry

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