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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Find the perimeter of the triangle. tagged by: BTGmoderatorLU ##### This topic has 1 expert reply and 0 member replies ### Top Member ## Find the perimeter of the triangle. In the figure above, triangle ABC is inscribed in the circle with center O, such that CD is perpendicular to AB. If the length of side AC is 5 and the radius equals r=25/8, find the perimeter of the triangle. (A) 14 (B) 15 (C) 16 (D) 20 (E) none of the above The OA is C. I'm confused with this PS question. Please, can any expert assist me with it? Thanks in advanced. ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Hello LUANDATO. Let's take a look at your question. As CD is perpendicular to AB then AD=DB. Let's name this lenght as "y". So, the right triangles ADC and BDC has two sides of the same lenght, so BC=AC=5. By the other hand, CO=r=25/8. Let's name OD as "x". We need to find "y" to get the perimeter. Using the Pythagoras theorem we have that: $$5^2=y^2+\left(\frac{25}{8}+x\right)^2\ \leftrightarrow\ 25=y^2+\frac{625}{64}+\frac{25}{4}x+x^2$$ and $$\left(\frac{25}{8}\right)^2=y^2+x^2\ \leftrightarrow\ y^2+x^2=\frac{625}{64}.$$ Replacing this last equation in the first one we have: $$25=\frac{625}{64}+\frac{625}{64}+\frac{25}{4}x\ \leftrightarrow\ 25=\frac{625}{32}+\frac{25}{4}x\ \leftrightarrow\ x=\frac{7}{8}.$$ Now, we can find the value of "y". $$y^2+\left(\frac{7}{8}\right)^2=\frac{625}{64}\ \leftrightarrow\ y^2=\frac{576}{64}\ \leftrightarrow\ y=3.$$ Now, the perimeter of the triangle is $$P=AC+AB+BC=5+2\cdot3+5=16.$$ So, the correct answer is C. I hope this explanation can help you. I'm available if you'd like a follow up. Regards. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now. • FREE GMAT Exam Know how you'd score today for$0

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