Common Tangents
Common Tangents
Common Tangents: If a line is tangent to two circles in the same plane then the line is called the common tangent. If the two circles are on the same side of the tangent then it is called a direct tangent otherwise if the two circles are on the other side of tangent it is called an indirect tangent,
The number of common tangents for concentric circles is zero. |
The number of common tangents for two circles touching internally is one. |
The number of common tangents for two intersecting circles is two. |
The number of common tangents for two circles touching externally is three out of which two are direct tangent and the third is an indirect tangent. |
The number of common tangents for two non intersecting and not touching circles is four. out of which two are direct and two are inditrect. | |
Illustration: Two circles touch externally at P and a common tangent touches them at A and B. Prove that
(i) The common tangent at P bisects AB (ii) AB subtends a right angle at P
Solution : Let the common tangent at P touches the common tangent AB at T AT = PT (1) [ Length of tangent from point T are equal] BT= PT (2) [ Length of tangent from point T are equal] From (1) and (2) We get AT = BT Hence T bisects AB In In adding (3) and (4)
In
Hence AB subtends angle of right angle at P |  |
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