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

Question

https://gmatclub.com/forum/download/file.php?id=54931 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. 1.png

GMATinsight · Answer

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

Answer: Option D

dimri10 · Answer

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.

NitishJain · Answer

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

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia