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A rectangle is inscribed in a circle so that the circle and rectangle

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A rectangle is inscribed in a circle so that the circle and rectangle  [#permalink]

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06 Sep 2018, 23:38
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A rectangle is inscribed in a circle so that the circle and rectangle touch at points A, B, C, and D only. What is the area of the circle?

(1) The sum of the diagonals of the rectangle is 8.

(2) $$AB + BC + CD + DA = 6 + 2\sqrt{7}$$

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Re: A rectangle is inscribed in a circle so that the circle and rectangle  [#permalink]

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07 Sep 2018, 00:40
Bunuel wrote:
A rectangle is inscribed in a circle so that the circle and rectangle touch at points A, B, C, and D only. What is the area of the circle?

(1) The sum of the diagonals of the rectangle is 8.

(2) $$AB + BC + CD + DA = 6 + 2\sqrt{7}$$

Question : Area of CIrcle = ?

For this purpose, We need the radius of the rectangle = Diagonal of rectangle

Statement 1: The sum of the diagonals of the rectangle is 8

Both diagonals of rectangle are equal hence length of each diagonal of rectangle = 8/2 = 4

i.e Radius of circle = 4/2 = 2 hence Area of circle = π2^2 = 4π
SUFFICIENT

Statement 2:$$AB + BC + CD + DA = 6 + 2\sqrt{7}$$

i.e. Perimeter of rectangle = 6+2√7
i.e. l+b = 3+√7
But the diagonal can't be calculates as
Case 1: l = 3 and b = √7
Case 2: l = 1 and b = 2+√7

NOT SUFFICIENT

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A rectangle is inscribed in a circle so that the circle and rectangle  [#permalink]

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08 Sep 2018, 07:32
Bunuel wrote:
A rectangle is inscribed in a circle so that the circle and rectangle touch at points A, B, C, and D only. What is the area of the circle?

(1) The sum of the diagonals of the rectangle is 8.

(2) $$AB + BC + CD + DA = 6 + 2\sqrt{7}$$

S1 - AC+BD=8
AC=BD=4
We can find area of circle.

S2 - $$AB + BC + CD + DA = 6 + 2\sqrt{7}$$
$$2(AB+BC)=6 + 2\sqrt{7}$$
$$AB+BC = 3+\sqrt{7}$$
Insufficient.

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A rectangle is inscribed in a circle so that the circle and rectangle   [#permalink] 08 Sep 2018, 07:32
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