A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
Is the triangle that this question is speaking of unique, or could there be multiple cases?
"Let O be the circumcenter of ΔABC. Suppose OA and OB are perpendicular to each other. What is the measure of ∠C?
anonymous
 one year ago
Is the triangle that this question is speaking of unique, or could there be multiple cases? "Let O be the circumcenter of ΔABC. Suppose OA and OB are perpendicular to each other. What is the measure of ∠C?

This Question is Closed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Solving the problem is easy, but I just am worried that there could be multiple cases, one in which the triangle could be acute and one in which the triangle could be obtuse. I don't think this problem is possible were the triangle to be a right triangle.

phi
 one year ago
Best ResponseYou've already chosen the best response.2the angle at C is always 1/2 of the intercepted arc given OA and OB are perpendicular means the central angle is 90 degrees

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yep, that would be the case for an acute. I was then worried if it were possible, based on how the problem had to be constructed, that you could have C be inside the angle .

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1437855911900:dw

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.0. i lost my graph with cancel xDDDDDDD

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oops, haha. I hate that x_X

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0And yeah, I thought it might be possible but I wasn't sure. If it's not possible then I don't want to claim multiple cases.

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.0dw:1437856026860:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I know the circumcenter is outside the triangle if the triangle is obtuse. But since the circumcenter is the intersection of the perpendicular bisectors, I couldn't conclude whether or not I could still have the perpendicular bisectors intersect while OA still remainded perpendicular to OB.

phi
 one year ago
Best ResponseYou've already chosen the best response.2the other case has <C = 135 deg

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.0the thing is its not unique triangle but a unique angle :D xD

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ah. So there only is one case then?

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.0it need not to be a bisector though :O

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So what are you saying then? xD

phi
 one year ago
Best ResponseYou've already chosen the best response.2your picture with C forming an obtuse angles meets the given conditions. O is the circumcenter OA is 90 deg to OB so it is valid... < C would be 135 in that case

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.0u already set two cases xD

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.0but 90+ obtuse noway

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0No, I agree, phi. But would O still be the intersection of the perpendicular bisectors under the given conditions? dw:1437856512007:dw I'm not sure if this picture is possible. I was trying to draw it out on my own and couldnt show that those perpendicular bisectors would still hit the circumcenter O. Sorry if my question isn't clear, lol.

phi
 one year ago
Best ResponseYou've already chosen the best response.2yes, the perpendicular bisectors of the sides will meet at the circumcenter (but outside of the triangle)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay, so I do need two cases. Yeah, I couldnt prove it to myself that I need the answers of both 45 and 135 degrees, wanted to confirm :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1437856799729:dw Two triangles one acute and one obtuse, but both with the ability to fit the given conditions. That's what I was unsure of. But either way, I'll make sure to mention both cases :3

phi
 one year ago
Best ResponseYou've already chosen the best response.2for what it is worth, here is a figure I made using Geogebra (free and useful tool) where the radiuses are perpendicular, and thus the third angle is 135 degrees It shows the perpendicular bisectors of the 3 legs as blue lines that intersect at the circumcenter.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ah. Cool. I like that :) Yeah, our class has us using Geometer's Sketchpad, but that's not free :( I'll check out Geogebra ^_^

phi
 one year ago
Best ResponseYou've already chosen the best response.2each side of the triangle is a chord of the circumcircle, and the perpendicular bisectors of a chord always goes through the circle's center. in other words, it *has to work*

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That's interesting. Yeah, when you say that it definitely clears things up. Thanks again :)
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.