prove that if two circles are tangent externally then the common internal tangent bisects a common external tangent.
1 answer:
Explanation:
Consider the attached diagram.
Circles A and B have mutual tangents CF and DE that intersect at point F.
We know that the two tangents to a circle from an external point are congruent, so ...
FE≅ FC
FD ≅ FC
By the transitive property of congruence, both segments congruent to FC are congruent to each other:
FD ≅ FE
Therefore, CF is a bisector of DE.
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