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.
In triangle ABC, AB = AC and angle A = 60o. A semicircle with diamet
[#permalink]
17 Feb 2025, 01:12
17 Feb 2025, 01:12
Expert Reply
00:00
Question Stats:
100% (01:55) correct
0% (00:00) wrong based on 3 sessions
Hide Show timer Statistics
In triangle ABC, AB = AC and angle A = 60°. A semicircle with diameter along the side BC is drawn. If length of the arc of the semi-circle is 50π, what is the perimeter of the triangle?
A. 100
B. 200
C. 300
D. 400
E. 500
A. 100
B. 200
C. 300
D. 400
E. 500
- Part of the project: GRE Quant & Verbal ADVANCED Daily Challenge 2025 NEW Edition - Gain 20 Kudos & Get FREE Access to GRE Prep Club TESTS
- Also replying to the unanswered questions
Re: In triangle ABC, AB = AC and angle A = 60o. A semicircle with diamet
[#permalink]
11 Mar 2025, 11:21
11 Mar 2025, 11:21
Expert Reply
In triangle ABC , angle A is 60 degrees and $\(\mathrm{AB}=\mathrm{AC} \Rightarrow \angle \mathrm{B}=\angle \mathrm{C}=\frac{1}{2}(180-60)=60\)$ (When sides are equal, opposite angles are also equal and the sum of the angles of a triangle is 180 degrees). So, triangle ABC is an equilateral triangle.
Also we are given that a semi circle is drawn with diameter along the side $\(B C\)$, so the radius of the circle, say $\(r\)$, must be half of $\(B C\)$
The length of the arc of the semi circle $\(=\frac{1}{2}(2 \pi r)=\pi r=50 \pi \Rightarrow r=50\)$, so we get $\(B C=\)$ $\(2 \mathrm{r}=2 \times 50=100\)$
Finally, the perimeter of the triangle ABC is $\(3 \times\)$ Side $\(=3 \times 100=300\)$
Hence the answer is (C).
Also we are given that a semi circle is drawn with diameter along the side $\(B C\)$, so the radius of the circle, say $\(r\)$, must be half of $\(B C\)$
The length of the arc of the semi circle $\(=\frac{1}{2}(2 \pi r)=\pi r=50 \pi \Rightarrow r=50\)$, so we get $\(B C=\)$ $\(2 \mathrm{r}=2 \times 50=100\)$
Finally, the perimeter of the triangle ABC is $\(3 \times\)$ Side $\(=3 \times 100=300\)$
Hence the answer is (C).
gmatclubot
Re: In triangle ABC, AB = AC and angle A = 60o. A semicircle with diamet [#permalink]
11 Mar 2025, 11:21
Moderators:
