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Question:

For the two circles x² + y² = 16 and x² + y² - 2y = 0, there is/are:

Two pairs of common tangents

No common tangent

One pair of common tangents

Three common tangents

Solution:

Circle S1 is x² + y² = 16
Circle S2 is x² + y² - 2y = 0
Centre C1 is C1(0, 0) and radius R1 = 4
Centre C2 is C2(0, 1) and radius R2 = 1
Distance between Centres is C1C2 = 1
Since C1C2 < |R2 - R1|, Circle S2 is completely inside S1
=> No common tangents