A Moving Right Angle

★ 7/10plane geometry Inscribed Angle Circles vectors

Problem

Plane vectors $\vec{a}, \vec{b}, \vec{c}$ satisfy

|\vec{a}| = |\vec{b}| = 2, \qquad |\vec{c}| = 1, \qquad (\vec{a} - \vec{c})\cdot(\vec{b} - \vec{c}) = 0.

Find the range of possible values of $|\vec{a} - \vec{b}|$ .

Answer

Solution

Difficulty	7/10
Topics	plane geometry, Inscribed Angle, Circles, vectors

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