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Question

In trapezium ABCD, M¯¯¯¯¯¯¯¯¯AD,n¯¯¯¯¯¯¯¯BC are the points such that AMMD=BNNC=23.
The diagonal ¯¯¯¯¯¯¯¯AC intersects ¯¯¯¯¯¯¯¯¯¯¯MN at O. Then find the value of AOAC.

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Solution

In ABCD,¯¯¯¯¯¯¯¯AB||¯¯¯¯¯¯¯¯¯CD, M and N are the points on transversals AD and BC respectively
Also, AMMD=BNNC
MN||AB and AB||CD
MN intersects AC at O.
In ΔADC,MO||DC,Mε¯¯¯¯¯¯¯¯¯AD,Oε¯¯¯¯¯¯¯¯AC
AMMD=AOOC
But AMMD=23
AOOC=23
AOAO+OC=22+3
AOAC=25
666684_626528_ans_7df7fceeee0a4ea6a79f24d6a025cb6e.png

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