Trigonometry! Even in the circle

Geometry Level 2

Let A A , B B , C C and D D be the angles of a quadrilateral. If they are con-cyclic, then the value of cos ⁡ A \cos \ A + cos ⁡ B \cos \ B + cos ⁡ C \cos \ C + cos ⁡ D \cos \ D .


The answer is 0.

Manish Mayank by Manish Mayank , 20, India

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2 solutions

Deepak Kumar
Nov 25, 2014

Considering any cyclic quadrilateral ABCD,we have A+C=180 degree=>A=180-C=>CosA=-CosC=>CosA+CosC=0 .Similarly cosB+cosD=0.Hence answer is 0

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Manish Mayank
Nov 25, 2014

One of the possible cyclic quadrilateral is a rectangle. So I let A=B=C=D= 9 0 0 90^0 thus, the value of cos ⁡ A \cos \ A + cos ⁡ B \cos \ B + cos ⁡ C \cos \ C + cos ⁡ D \cos \ D = 0

1 Helpful 0 Interesting 0 Brilliant 0 Confused

I solved it using the same method.

Muhammad Mahdi Shahriar Sakib - 6 years, 6 months ago

To do it using cyclic quadrilateral property is the correct solution.

Kartik Sharma - 6 years, 6 months ago

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Yes, I know. I just expressed my views about the question.

Manish Mayank - 6 years, 6 months ago

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