My Math Forum About Triangles in Cones

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 July 13th, 2013, 07:20 PM #1 Newbie   Joined: Jul 2013 Posts: 1 Thanks: 0 About Triangles in Cones Consider all triangles which are on the plane of the axis of a cone, have the apex of the cone as one of their vertices, and the diameter of the base as their bases. Do they have equal areas, are somehow related, or share any interesting properties? If so, could you show me the proof?
 July 14th, 2013, 05:06 AM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond Re: About Triangles in Cones How many such triangles may be constructed?
July 14th, 2013, 08:13 AM   #3
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Hello, Correia!

Quote:
 Consider all triangles which are on the plane of the axis of a cone, have the apex of the cone as one of their vertices, and the diameter of the base as their bases. Do they have equal areas, are somehow related, or share any interesting properties? If so, could you show me the proof?

If It is a right circular cone, all the triangles are congruent.

If it is an oblique circular cone, all the triangles have equal areas.

If it is an elliptic cone (right or oblique) . . . ???

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