Quadrilateral pt. 2

Geometry Level 4

In a quadrilateral A B = B C = 13 AB=BC=13 , ∠ A B C = 10 2 ∘ \angle ABC=102^\circ and angle A D C = 12 9 ∘ ADC=129^\circ .

What is the length of B D BD ?

6.5 13 16 26 10 7 1

Dragan Marković by Dragan Marković , 26, Serbia

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1 solution

Dragan Marković
Apr 26, 2016

Lets describe a circle around the quadrilateral ABCD with the center in point B. angle ABC is the center angle for that circle so the periphery angle is 51º. let that angle be AEC=51º. Since AEC+ADC=180º we have a cyclic quadrilateral=> so point D is on the circle with the center in B=> Therefore, we get that AB=BC=BD=13

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Really a nice approach.(+1)

Rakshit Joshi - 5 years, 1 month ago

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Much appreciated ! :)

Dragan Marković - 5 years, 1 month ago

Very simple, interesting and intelligent solution. Congratulations.

Niranjan Khanderia - 5 years, 1 month ago

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Thank you very much!

Dragan Marković - 5 years, 1 month ago

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