Let the line x + y = 1 meet the circle x 2 + y 2 = 4 at the points A and B . If the line perpendicular to A B and passing through the mid point of the chord A B intersects the circle at C and D , then

Question

Let the line x + y = 1 meet the circle x 2 + y 2 = 4 at the points A and B . If the line perpendicular to A B and passing through the mid point of the chord A B intersects the circle at C and D , then the area of the quadrilateral ADBC is equal to :

TestHub · Accepted Answer

By solving x = y with circle We get ​ C ( 2 ​ , 2 ​ ) D ( − 2 ​ , − 2 ​ ) ​ By solving x + y = 1 with circle x 2 + y 2 = 4 we set ​ A ( 2 1 + 7 ​ ​ , 2 1 − 7 ​ ​ ) & B ( 2 1 − 7 ​ ​ , 2 1 + 7 ​ ​ ) ​ ∴ Area of Quadrilateral ACBD = 2 × Area of △ BCD ​ = 2 × 2 1 ​ ​ 2 ​ 2 1 − 7 ​ ​ − 2 ​ ​ 2 ​ 2 1 + 7 ​ ​ − 2 ​ ​ 1 1 1 ​ ​ = 2 14 ​ ​

Mathematics - Circle Question with Solution | TestHub

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