The area of a cyclic Quadrilateral A BC D is 4 3 3 . The radius of the circle circumscribing the Quadrilateral is 1 . If A B = 1 , B D = 3 then the value of 3 ⋅ BC ⋅ C D is

Question

The area of a cyclic Quadrilateral A BC D is 4 3 3 ​ ​ . The radius of the circle circumscribing the Quadrilateral is 1 . If A B = 1 , B D = 3 ​ then the value of 3 ⋅ BC ⋅ C D is

TestHub · Accepted Answer

3 = 1 + A D 2 − 2 × 1 × A D × 2 − 1 ​ A D 2 + A D − 2 = 0 ( A D + 2 ) ( A D − 1 ) = 0 ⇒ A D = 1 ∠ BO D = 2 C cos 2 C = 2 − 1 ​ ⇒ C = 6 0 ∘ , A = 12 0 ∘ ∴ 2 1 ​ × 1 × 1 × 2 3 ​ ​ + 2 1 ​ × BC . C D × 2 3 ​ ​ = 2 3 3 ​ ​ B BC . C D = 2

Mathematics - Properties of Triangle Question with Solution | TestHub

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