Jump to content
Urch Forums

On triangles inscribed in circles


jjaacc

Recommended Posts

Length of the arc ABC = 24 (given)

Let O be the centre of the circle..OA = OB = OC = radius

arc ABC = arc AB+ arc BC

arc OAB = 120 degrees => length AB = 120/360(2*pi*r)

arc OBC = 120 degrees => length BC = 120/360(2*pi*r)

summing up, we get 2/3(2*pi*r) = 24

=> 2r = 36/pi = 11.46 (Ans C)

 

Note:

For the geometry, draw a line from O to the midpoint of AB, u'll get a 30-60-90 triangle and u can compute arc OAB : 120 degrees

Link to comment
Share on other sites

should be simpler really...

 

you know that the length of an arc is directly proportional to the inscribed angle creating it. further we know that the triangle is equilateral so all angles are the same and thus the three arcs will have the same length (12).

from here you just plug into the pi*d = circum (36=pi*d ~ 11)

Link to comment
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Reply to this topic...

×   Pasted as rich text.   Restore formatting

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

×
×
  • Create New...