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Question

# In triangle ABC ; M is mid-point of AB, N mid-point of AC and D is any point in base BC. Then:

A
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B
MN divides AD in the ratio 1:3
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C
MN divides AD in the ratio 1:2
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D
MN divides AD in the ratio 1:4
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Solution

## The correct option is A MN bisects ADIn △ABC, M is mid point of AB and N is mid point of ACD is any point of BCNow, Join AD and MN such that they met at OIn △ABCM is mid point of AB and N is mid point point of ACHence, MN∥BC and MN=12BCNow, In △ABDMO∥BC and M is mid point of ABThus, O is mid point of ADHence, MN bisects AD

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