Question

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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Answer 1

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