Theorem 5. If two circles touch each other internally or externally, the point of contact lie on the line joining their centres.
Given:- Two circles with centres O1 and O2 touch internally in figure (i) and externally in figure (ii) at A.
To prove: - The points O1, O2 and A lie on the same line.
Construction:- A common tangent PQ is drawn at A.
Proof: - In figure (i) (PA is tangent to the two circles)
O1, O2 and A are collinear.
In figure (ii) (PA is tangent to the circles)
i.e. from a linear pair
O1, O2 and A lie on the same line.
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