NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 16:32 It is currently 25 Apr 2024, 16:32
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT 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

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Right angled triangle in a circle

User avatar
gmatter0913
Manager
Manager
Joined: 12 Mar 2010
Posts: 219
Own Kudos [?]: 1215 [0]
Given Kudos: 86
Concentration: Marketing, Entrepreneurship
GMAT 1: 680 Q49 V34
Send PM
Right angled triangle in a circle [#permalink] New post   07 Feb 2012, 13:09
If a right angled triangle is inscribed in a circle, is it necessary for the hypotenuse of the right triangle to be the diameter of the circle? I know that the vice-versa is true.



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619022 [1]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: Right angled triangle in a circle [#permalink] New post   07 Feb 2012, 13:53
1
Kudos
Expert Reply
bsaikrishna wrote:
If a right angled triangle is inscribed in a circle, is it necessary for the hypotenuse of the right triangle to be the diameter of the circle? I know that the vice-versa is true.


A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle.

The reverse is also true: if the diameter of the circle is also the triangle’s side, then that triangle is a right triangle.

For more on this topic please check Circle chapter of Math Book: math-circles-87957.html

Hope it helps.
User avatar
gmatter0913
Manager
Manager
Joined: 12 Mar 2010
Posts: 219
Own Kudos [?]: 1215 [0]
Given Kudos: 86
Concentration: Marketing, Entrepreneurship
GMAT 1: 680 Q49 V34
Send PM
Re: Right angled triangle in a circle [#permalink] New post   07 Feb 2012, 15:11
Thank you so much for all your replies. You've been a great help to me. :)
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14823
Own Kudos [?]: 64923 [0]
Given Kudos: 426
Location: Pune, India
Send PM
Re: Right angled triangle in a circle [#permalink] New post   07 Feb 2012, 22:55
Expert Reply
bsaikrishna wrote:
If a right angled triangle is inscribed in a circle, is it necessary for the hypotenuse of the right triangle to be the diameter of the circle? I know that the vice-versa is true.



You can figure this out by drawing a diagram.
Attachment:
Ques3.jpg

Look how the angle is increasing as you go higher up. Hence for every length of the minor arc, there is a unique inscribed and central angle. The right triangle's hypotenuse will be the largest length of the chord i.e. a diameter and its central angle will be 180 giving the inscribed angle as 90.

Also, length of arc = (Central angle/360) * 2*pi*r
Since inscribed angle is 90, central angle is 180.

length of arc = 180/360 * (2*pi*r)
length of arc = pi*r
i.e. you get a semi circle. So the chord (the hypotenuse of the right triangle) must be the diameter.



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
GMAT Club Bot
gmatclubot
Re: Right angled triangle in a circle [#permalink]
07 Feb 2012, 22:55
Moderator:
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions