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# If point O is the center of the circle as shown in the figure, what is

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Math Expert
Joined: 02 Sep 2009
Posts: 65061
If point O is the center of the circle as shown in the figure, what is  [#permalink]

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02 Jun 2020, 04:11
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25% (medium)

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91% (01:05) correct 9% (01:12) wrong based on 34 sessions

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If point O is the center of the circle as shown in the figure, what is the area of the circle (in sq. cm.) ?

(1) Length of the major arc ACB is 9π cm.
(2) Area of ΔOAB = 18 sq. cm.

Attachment:

1.png [ 14.64 KiB | Viewed 370 times ]

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If point O is the center of the circle as shown in the figure, what is  [#permalink]

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02 Jun 2020, 04:20
Bunuel wrote:

If point O is the center of the circle as shown in the figure, what is the area of the circle (in sq. cm.) ?

(1) Length of the major arc ACB is 9π cm.
(2) Area of ΔOAB = 18 sq. cm.

Attachment:
1.png

Question: Area = ? i.e. Radius = ?

Statement 1: $$(\frac{3}{4})2πr = 9π$$

SUFFICIENT

STatement 2: Area of ΔOAB = 18 sq. cm.

i.e. $$(\frac{1}{2})r^2 = 18$$

i.e. r = 6

SUFFICIENT

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If point O is the center of the circle as shown in the figure, what is  [#permalink]

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Updated on: 02 Jun 2020, 12:13
i believe it is D. both sufficient

1. USE CIRCUMFERENCE FORMULA
9PIE= PIE*Diameter*3/4 (270/360). solve for Diameter and find Radius for area

2. use area formula:
PIE*R^2*1/4 (90/360)=18^2. Solve for R AND FIND TOTAL AREA

SO, I SEE IF IT WAS A PS I WAS WRONG. I SEE IT IS THE AREA OF THE TRIANGLE.

Originally posted by dimri10 on 02 Jun 2020, 04:24.
Last edited by dimri10 on 02 Jun 2020, 12:13, edited 1 time in total.
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Re: If point O is the center of the circle as shown in the figure, what is  [#permalink]

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02 Jun 2020, 06:56
IMO D

Area = π(r^2); So we need to find r.

Stmt 1: Length of the major arc ACB is 9π

angle of major arc / 360 = Circumference of arc /Circumference of circle

270/360 = 9π/2πr

Sufficient

Stmt 2: Area of ΔOAB = 18 sq. cm
==>1/2(OA * OB) = 18
OA=OB =r
==> r^2 = 18 *2
Sufficient
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Re: If point O is the center of the circle as shown in the figure, what is   [#permalink] 02 Jun 2020, 06:56