10. The bisector of interior ∠A of ΔABC meets BC in D and bisector of external ∠A
meets BC (produced) in E. Prove that BD/BE=CD/CE.
.
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To prove: BD/BE = CD/CE
Proof: In △ABC, AD bisects interior ∠A
∴ AB/AC = BD/DC (Angle bisector theorem) ..........1)
Similarly in △ABC, AE bisects exterior ∠A
∴ AB/AC BE/CE ...........2)
From equation (1) and (2)
AB/AC = BD/DC = BE/CE = CD/CE
Hence proved.
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