A triangle inscribed in a semicircle

Math Central

Quandaries & Queries

Subject: Limiting Cases in Geometry
Name: Benneth
Who are you: Student

Consider a triangle inscribed in a semicircle with a radius of R. What are the possible perimeters for the triangle?
And the areas?

Hi Benneth,

I think you are to inscribe the triangle so that one side is the diameter of the semicircle.

semicircle

The area of the triangle is one-half the base (2R) times the height (h). If A is at B then the height is zero. How large can the height be?

For the perimeter use the fact that angle CAB is a right angle and apply Pythagoras theorem.

Penny

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