O is the center of the semicircle. If angle BCD = 30 and BC =

Question

triacirc_q1.png O is the center of the semicircle. If angle BCO = 30 and BC = 6\sqrt{3} , what is the area of triangle ABO? A. 4\sqrt{3} B. 6\sqrt{3} C. 9\sqrt{3} D. 12\sqrt{3} E. 24\sqrt{3} Kudos for a correct solution .

hsbinfy · Answer

answer is C

angle ABC is right angled triangle and bc=6sqt3

so we can calculate other two sides AB and AC thrru 30:60:90 funda

so AC comes out to be 12 and AB=6

so AB=AO=6

FOR BO we can see ABO is a isoscles traingle and from that we can conclude ABO is an equitriangle with each side 6.

so area=sqt3 *6*6/4=9sqt3

FightToSurvive · Answer

Yes its C.

From the figure we can compute the diameter of the semi circle through 30-60-90 triangle, from that get 3 sides of ABO which is equilateral. 
Then simple formula sqrt (3)/4 (side)^2 which gives u C as the answer.

Posted from my mobile device

bhatiamanu05 · Answer

O is the center of the semicirlce than

OA = OB = OC all are radius.

angle BCO = 30 
angle ABC = 90 (semicircle)
angle BAC = 60 (sum of angles are 180)

angle OBC = angle BCO = 30 (equal sides)
angle ABO = angle BAO = 60 (equal sides)
so AOB is equilateral triangle

so AB = OA = OB = OC = x
Applying pythagorus in ABC triangle
x^2+(6sqrt(3))^2= 4x^2

3x^2 = 36*3
x^2 = 36

x =

so area of equilateral triangle = sqrt(3)/4*36

9sqrt(3)

peachfuzz · Answer

A triangle inscribed in a circle with the diameter as its hypotenuse is a right triangle. 
That means triangle ABO is an equilateral triangle with AB and AO as radiuses.

Using a 30 60 90 property of a triangle, the height of triangle ABO is 3sqrt(3)
(1/2)(6)(3sqrt(3))
=  9\sqrt{3}

Answer: C

Temurkhon · Answer

ABC is right triangle with 1:sqrt3:2 ratio of its sides

area of ABC=(6*6*sqrt3)/2=18*sqrt3

BO is a median splting ABC into two triangles with equal area

18*sqrt3/2=9*sqrt3

C

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION: triacirc_explanation.png FAQ: How do we know that angle ABC is a right angle? There are two things we need to know to understand the right angle 1. We are told O is the center, and any line that goes from the center of a circle to the circle edge is a radius. 2. When you have an inscribed angle in a triangle that connects to the diameter, that inscribed angle is always 90 degrees. The related lesson about circle properties linked below covers this topic in more detail.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

O is the center of the semicircle. If angle BCD = 30 and BC =

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

My Rewards

GMAT Problem Solving (PS) Questions

O is the center of the semicircle. If angle BCD = 30 and BC =

Prep Toolkit

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

My Rewards