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ABC, L is the mid point of BC and Mis the mid point of AL(C) In A ABCMintersects AC at N, LP | BN.Prove that: AN= =w |
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Answer» Through D,Draw DK||BN.In triangleADK, M is the mid-point of ADand MN||DK.Therefore, N is the mid-point of AK.Hence, AN=NK.............(i)In triangleBCN,D is the mid-point ofBCand BN||DK.Therefore,K is the mid-point of NC.Hence, KC=NK.............(ii)From (i) and (ii),AN=NK=KC..............(iii)Now, AC=AN+NK+KCAC=AN+AN+ANAC=3ANtherefore, AN=1/3AC. |
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