SOLUTION: Alex is decorating a circular cake. She wants to place a triangle with the longest possible side within the circle. The radius of the circle is 4.5 inches. What can the longest sid

Question 1154728: Alex is decorating a circular cake. She wants to place a triangle with the longest possible side within the circle. The radius of the circle is 4.5 inches. What can the longest side of the triangle measure?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

A chord of a circle is a segment that has both endpoints on the circle. The longest chord of any circle is always the diameter. Since the radius is r = 4.5, this means the diameter is d = 2*r = 2*4.5 = 9

By Thales's Theorem, this diameter is also the hypotenuse of the right triangle that is inscribed in the circle. By "inscribed", I mean that the triangle is completely contained within the circle, and there are no parts spilling out. Also, the three vertices of the inscribed triangle are on the circle.

Answer: 9 inches

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