Tangency of line y=mx+c to circle x²+y²=r² (Liney=mx+ctouchescirclex²+y²=r²iffdistancefrom(0,0))
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Line y=mx+c touches circle x²+y²=r² iff distance from (0,0) to line equals r: |c|/√(1+m²)=r ⇔ c²=r²(1+m²).
What each symbol means
| Symbol | What it stands for |
|---|---|
| r | Circle radius |
| m, c | Line parameters |
When to use this
Circle centered at origin; shift coordinates if center moved.