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KVPY2015MathematicsProperties of Triangles

Suppose A B C D E F is a hexagon such that A B=B C=C D=1 and D E=E F=F A= 2. If the vertices A, B, C, D, E, F are concyclic, the radius of the circle passing through them is.

Options

  1. A5 2
  2. B[ ] 7 3
  3. C[ ] 11 5
  4. D2

Correct answer

B. [ ] 7 3

Step-by-step solution

+ =120^ So, array l A=120^ ABCDEF are concyclic A = 120^ = 1²+2²-F B² 2(1)(2) -1 2 = 5-F B² 2(2) F B²=7 F B= 7 array Again by cosine rule array l ( + )= r²+r²-7 2 r² - 1 2 = 2 r²-7 2 r² 3 r²=7 r= 7 3 array

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