Transformations
Move the picture until the problem is easy.
At the highest level you stop solving the configuration and start changing it. A homothety (scaling about a centre) maps lines to parallel lines and circles to circles — the natural response to tangent circles or parallel lines.
A spiral similarity (rotation plus scaling) explains almost every 'two similar triangles hiding in the figure' situation; its centre is the second intersection of two well-chosen circumcircles.
Inversion is the heavy artillery: sends circles through the centre to straight lines. Choose the centre where the most circles meet, and a tangle of circles unfolds into lines.
Train it on Lemma
Transformations unlocks at Level 8 of Lemma's eight-level ladder, with lessons that teach it and drills that make it stick. 78 lessons, 624 curated problems and unlimited generated practice at six difficulties. Free to start — no card, no trial clock.
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