#### Presentation Title

The Largest Area of an Outscribed Equilateral Triangle

#### Presentation Type

Oral Presentation

#### School

School of Sciences and Social Sciences

#### Discipline

Mathematics

#### Mentor

Vincent Ferlini

#### Date & Time

April 9th at 3:15 PM - 4:15 PM

#### Location

David F. Putnam Science Center, Room 102

#### Abstract

Triangle DEF is an *outscribed triangle* of ABC if each edge of DEF contains one and only one vertex of ABC . If all sides of DEF are of equal length then DEF is called an *outscribed equilateral triangle* of ABC . This presentation will show that for a given triangle ABC, there exists an outscribed equilateral triangle DEF with maximum area. Computations will be justified both theoretically and through the use of special geometry software. Determining the maximum area and constructing DEF with a straightedge and compass will also be included.

The Largest Area of an Outscribed Equilateral Triangle

David F. Putnam Science Center, Room 102

Triangle DEF is an *outscribed triangle* of ABC if each edge of DEF contains one and only one vertex of ABC . If all sides of DEF are of equal length then DEF is called an *outscribed equilateral triangle* of ABC . This presentation will show that for a given triangle ABC, there exists an outscribed equilateral triangle DEF with maximum area. Computations will be justified both theoretically and through the use of special geometry software. Determining the maximum area and constructing DEF with a straightedge and compass will also be included.