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# What is the perimeter of the sector in the circle above if angle x is

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Math Expert
Joined: 02 Sep 2009
Posts: 52971
What is the perimeter of the sector in the circle above if angle x is  [#permalink]

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07 Sep 2018, 00:31
00:00

Difficulty:

25% (medium)

Question Stats:

81% (00:45) correct 19% (01:27) wrong based on 19 sessions

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What is the perimeter of the sector in the circle above if angle x is 90°? (Assume O is the center)

(1) The area of the circle is 4π.
(2) The minor arc AC has length π.

Attachment:

image002.jpg [ 3.36 KiB | Viewed 281 times ]

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Re: What is the perimeter of the sector in the circle above if angle x is  [#permalink]

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07 Sep 2018, 01:45
Bunuel wrote:

What is the perimeter of the sector in the circle above if angle x is 90°? (Assume O is the center)

(1) The area of the circle is 4π.
(2) The minor arc AC has length π.

Attachment:
image002.jpg

Question: Perimeter of the sector = Length of arc + 2*Radius $$= (1/4)2πr+2r =$$?

Statement 1: The area of the circle is 4π.

i.e. $$(1/4)πr^2 = 4π$$
This gives us the radius hence

SUFFICIENT

Statement 2: The minor arc AC has length π

$$(1/4)2πr = π$$

This gives us the radius hence

SUFFICIENT

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Re: What is the perimeter of the sector in the circle above if angle x is   [#permalink] 07 Sep 2018, 01:45
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