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 ]

AD + BD + CE = AF + BE + CF

$\dpi{120} \large \Rightarrow$      ( AD + BD ) + CE = ( AF + CF ) + BE

$\dpi{120} \large \Rightarrow$           AB + CE = AC + BE

$\dpi{120} \large \Rightarrow$           AB + CE = AB + BE                       [ $\dpi{120} \large \therefore$  AC = AB ]

$\dpi{120} \large \Rightarrow$                   CE = BE                   [ cancel AB from both the sides ]

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