Math CentralQuandaries & Queries


Question from Kamerson:

i have been given a problem with a 30-60-90 triangle and a circle inscribed with a radius of 2 and was told to find the perimeter of the triangle

Hi Kamerson,

You can solve this problem using two facts.

First for a 30-6--90 triangle the lengths of the sides are in the ratio $1:2:\sqrt{3}.$

For the second fact I need to draw a diagram.


P is the center of the circle and D, E and F are points of tangency. The fact I see is that triangles PFC and DPC are congruent.

Can you solve the problem now?


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