Gigoujeu's Theorem
Question:
Given a point A on the circle (x-a)2+y2=R2 (O), draw tangents to the
circle x2+y2=1 (0') ; Join the points of contact of these tangents;
Draw the tangent to O at A;
One wants the LOCUS of the point of intersection of that tangent with the chord of contacts on the
circle O'
Answer:
a2x4+
2a(R2-a2-1)x3
+(a2 y2+ a4+4a2-2a2R2+ (R2-1)2)x2
+2a (( R2-1 )y2 +R2-a2-1)x
+((R2-1)^2-a2R2)y2+ a2=0
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