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प्रश्न
Prove that the external bisector of an angle of a triangle divides the opposite side externally n the ratio of the sides containing the angle.
उत्तर
In ΔABC, CE || AD
∴ `"BD"/"CD" = "AB"/"AE"`.....(i)
(By Basic Proportionality theorem)
AD is e bisector of ∠CAF
∠FAD = ∠CAD......(ii)
Since CE || AD
Therefore,
∠ACE = ∠CAD......(iii) ...(alternate angles)
∠AEC = ∠FAD......(iv) ...(corresponding angles)
From (ii) and (iii) and (iv)
∠AEC = ∠ACE
In ΔAEC,
∠AEC = ∠ACE
AC = AE ......(v) ...(Equal angles have equal sides opposite to them)
From (i) and (v)
`"BD"/"CD" = "AB"/"AC"`.
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