Understand the problem

let O be a point inside a parallelogram ABCD such that \(\angle AOB+\angle COD =180\) prove that \(\angle OBC =\angle ODC\)

Source of the problem
C.M.I (Chennai mathematical institute UG-2019 entrance   
Topic
Geometry 

Difficulty Level

5 out of 10

Start with hints

Do you really need a hint? Try it first!

 

Draw a clear image of the given problem  

 

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

 

 

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

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

 

 

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

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

 

 

Connected Program at Cheenta

I.S.I. & C.M.I. Entrance Program

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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