The interior angle bisector of angle B, and the exterior bisector of angle C of triangle ABC meet at D. Through D, a line parallel to CB meet AC at L and AB at M. If LC = 5 and MB = 7 find LM. Justify your result
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If The interior angle bisector of∠B, and the exterior bisector of ∠C of ΔABC meet at D and DM ║ CB cut AC at L & AB at M such that LC = 5 & MB = 7 then LM = 2
Step-by-step explanation:
∠1 = ∠2 ( bisector of ∠B)
∠2 = ∠3 ( as DM ║ BC)
=> ∠1 = ∠3
=> in Δ BDM
DM = MB
MB = 7
=> DM = 7
∠4 = ∠5 ( Bisector of ∠C)
∠5 = ∠LDC ( as DM ║ BC)
=> ∠4 = ∠LDC
in Δ LDC
=> DL = LC
LC = 5
=> DL = 5
DM = DL + LM
=> 7 = 5 + LM
=> LM = 2
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