Maths / Circles / Length of Tangents to a Circle

QUESTION
 
In fig. if AB = AC, prove that BE = EC.
EXPLANATION
Explain TypeExplanation Content
Text

Solution    As lengths of tangents from an external point to a circle are equal.

                        AD = AF            [ lengths of the tangents from point A ]

                        BD = BE            [ lengths of the tangents from point B ]

                        CE = CF            [ lengths of the tangents from point C ]

Adding the above, we get

               AD + BD + CE = AF + BE + CF

large Rightarrow      ( AD + BD ) + CE = ( AF + CF ) + BE

large Rightarrow           AB + CE = AC + BE                 

large Rightarrow           AB + CE = AB + BE                       [ large therefore  AC = AB ]

large Rightarrow                   CE = BE                   [ cancel AB from both the sides ]

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