GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
The sides of equilateral ABD are tangent to a circle with c
[#permalink]
05 Jan 2021, 09:36
05 Jan 2021, 09:36
Expert Reply
00:00
Question Stats:
90% (01:40) correct
9% (00:45) wrong based on 11 sessions
Hide Show timer Statistics
Attachment:
GRE The sides of equilateral.jpg [ 17.03 KiB | Viewed 1471 times ]
The sides of equilateral \( \triangle ABD\) are tangent to a circle with center O. If \(AB = 12 \sqrt{3}\) and \(OD = 12\), the circumference of the circle is
A. \(6 \pi\)
B. \(12 \pi\)
C. \(6 \pi \sqrt{3}\)
D. \(12 \pi \sqrt{3}\)
E. \(24 \pi\)
Kudos for the right answer and explanation
Re: The sides of equilateral ABD are tangent to a circle with c
[#permalink]
06 Jan 2021, 00:14
06 Jan 2021, 00:14
1
The triangle is an equilateral triangle.
The formulas for equilateral triangles are : (a- side of the triangle)
The in-radius of the equilateral triangle OC= \(\frac{a}{2\sqrt{3}}\)
The circum-radius of the equilateral triangle OA-OB-OD= \(\frac{a}{\sqrt{3}}\)
Side is given as
\(AB = 12 \sqrt{3}\)
So OC = \(\frac{12\sqrt{3}\ }{ 2\sqrt{3}\}\)
OC = 6
Circumference = \(2 * pi * radius\) = \(2*pi*6\) = \(12pi\)
Answer B
The formulas for equilateral triangles are : (a- side of the triangle)
The in-radius of the equilateral triangle OC= \(\frac{a}{2\sqrt{3}}\)
The circum-radius of the equilateral triangle OA-OB-OD= \(\frac{a}{\sqrt{3}}\)
Side is given as
\(AB = 12 \sqrt{3}\)
So OC = \(\frac{12\sqrt{3}\ }{ 2\sqrt{3}\}\)
OC = 6
Circumference = \(2 * pi * radius\) = \(2*pi*6\) = \(12pi\)
Answer B
Re: The sides of equilateral ABD are tangent to a circle with c
[#permalink]
06 Jan 2021, 09:21
06 Jan 2021, 09:21
1
As ABD is an equilaeral and circle is inscribed in the equilateral,
OC : OD : CD = 1:2: sqrt(3)
OD is 12 , so OC is 6.
The circumference of the circle o is 2x pi x OC = 2 x pi x 6
=12pi
Answer : B
OC : OD : CD = 1:2: sqrt(3)
OD is 12 , so OC is 6.
The circumference of the circle o is 2x pi x OC = 2 x pi x 6
=12pi
Answer : B
