6.5.1 Common Tangents (I)
A common tangent to two circles is a straight line that touches each of the circles at only one point.
1. Intersect at two points
(a) Circles of the same size
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Number of common tangents
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Properties of common tangents
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Two common tangents:
AB and CD
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AC = BD
AB = CD
AB parallel to // OR parallel to // CD
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(b) Circles of different sizes
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Number of common tangents
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Properties of common tangents
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Two common tangents:
ABE and CDE
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AB = CD
BE = DE
OA // RB
OC // RD
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2. Intersect at one point
(a) Circles of the same size
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Number of common tangents
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Properties of common tangents
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Three common tangents:
AB, CD and PQ
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AC = PQ = BD
AB = OR = CD
AB // OR // CD
AC // PQ // BD
PQ perpendicular to OR
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(b) Circles of different sizes
(i) External contact
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Number of common tangents
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Properties of common tangents
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Three common tangents:
ABE, CDE and PQ
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AB = CD
BE = DE
OA // RB
OC // RD
PQ perpendicular to ORE
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(ii) Internal contact
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Number of common tangents
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Properties of common tangents
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One common tangent: PQR
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ONQ perpendicular to PR
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