Arcs.... im stuck :(

G

Guest

Guest
Ok... i am totally stuck on these problems... the given is "Triangle ABC is inscribed in circle O"
Then it says to "name the arcs in order of size (Hint: the sum of the measures of the angles of a triangle is 180."

Here's an example of one of the questions:
The measure of angle A = 90; angle B=50 and angle C=40
___?____<____?____<____?_____

So now im not sure of what to put the answers that i had were wrong ( i put BC<AC<CA) Can anyone help me please? Thank you :wink:
 
Ainsley said:
Ok... i am totally stuck on these problems... the given is "Triangle ABC is inscribed in circle O"
Then it says to "name the arcs in order of size (Hint: the sum of the measures of the angles of a triangle is 180."

Here's an example of one of the questions:
The measure of angle A = 90; angle B=50 and angle C=40
___?____<____?____<____?_____

So now im not sure of what to put the answers that i had were wrong ( i put BC<AC<CA) Can anyone help me please? Thank you :wink:
Click to expand...

Look carefully at the diagram of triangle ABC inscribed in the circle. The largest arc will be opposite the largest angle (and defined by the OTHER TWO points of the triangle). That is, IF the largest angle of the triangle were at C, then arc AB would be opposite it and would be the largest arc.
 
THANK YOU SO MUCH!!!!!!! I understand it now. You're awesome :mrgreen:
 
i am totally stuck on these problems... the given is "Triangle ABC is inscribed in circle O"
Then it says to "name the arcs in order of size (Hint: the sum of the measures of the angles of a triangle is 180."

Here's an example of one of the questions:
The measure of angle A = 90; angle B=50 and angle C=40
___?____<____?____<____?_____

So now im not sure of what to put the answers that i had were wrong ( i put BC<AC<CA) Can anyone help me please? Thank you :wink:

Since the largest arc will be opposite the largest angle, you almost have the right side sequence but the wrong arrows.

BC>AC>AB
 
Hello, Ainsley!

My eternal question: Did you make a sketch?

Triangle ABC is inscribed in circle O.

\(\displaystyle \angle A\,=\,90^o,\;\angle B\,=\,50^o,\;\angle C\,=\,40^o\)

Name the arcs in order of size.

___?____<____?____<____?_____
Click to expand...
Code: 
              A 
              o * *
          * / 90\     *
        *  /      \     *
       *  /         \    *
         /            \
      * / 50         40 \ *
    B o - - - - - - - - - o C
      *                   *

       *                 *
        *               *
          *           *
              * * *
Can you see which is the smallest arc? . . . the largest arc?
 
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