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Geometry problem - CMI Entrance 2019

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Understand the problem

[/et_pb_text][et_pb_text _builder_version="3.27.4" text_font="Raleway||||||||" background_color="#f4f4f4" custom_margin="10px||10px" custom_padding="10px|20px|10px|20px" box_shadow_style="preset2"]let O be a point inside a parallelogram ABCD such that \(\angle AOB+\angle COD =180\) prove that \(\angle OBC =\angle ODC\)

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C.M.I (Chennai mathematical institute UG-2019 entrance   

[/et_pb_accordion_item][et_pb_accordion_item title="Topic" _builder_version="3.22.4" open="off"]Geometry 

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5 out of 10

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challenges and thrills of pre college mathemetics
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Start with hints

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Do you really need a hint? Try it first!

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Draw a clear image of the given problem  

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 translate  ABCD along the vector AD SO A' and D are the same , and  so that B' and C are the same 

 

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now , \(\angle COD +\angle CO'D=\angle COD+\angle A'O'D' =180 \)

so OCO'D is cyclic . therefore \(\angle OO'C =\angle ODC\)

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     Also , vector BC and OO' both equal AD so OBCO' is parallelogram . therefore 

\(\angle OBC =\angle OO'C=\angle ODC \)

 

 

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Connected Program at Cheenta

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Indian Statistical Institute and Chennai Mathematical Institute offer challenging bachelor’s program for gifted students. These courses are B.Stat and B.Math program in I.S.I., B.Sc. Math in C.M.I.

The entrances to these programs are far more challenging than usual engineering entrances. Cheenta offers an intense, problem-driven program for these two entrances.

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Similar Problem

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