Hidden circle I: fixed chord, fixed angle

Overview

Points seeing a fixed segment at a fixed angle lie on an arc.

Explanation

Fixed chord AB and fixed angle θ: locus of P with ∠APB = θ is an arc (both sides of AB).
When a problem never draws the circle but conditions match, call it a hidden circle.
Radius R = AB / (2 sin θ); larger θ → smaller radius, tighter arc.

How to use

Drag P with fixed ∠APB; adjust θ to reshape the dashed circle.

Knowledge points

• Circles
• Hidden circles