3.+Entree

=MAIN COURSE: Example Task (MP2) =

These three Japanese Temple Geometry problems lead to our next investigation Hidetoshi and Rothman, 2008,Sacred Mathematics: Japanese Temple Geometry, pg 67 ||
 * [[image:triangle_with_circles.png width="398" height="349"]]

Given an equilateral triangle of side 1 unit, show that the diameters of the circles are approximately 0.26794 units. ||  || Hidetoshi and Rothman, 2008,Sacred Mathematics: Japanese Temple Geometry, pg 67 ||
 * [[image:pentagon_with_circles.png width="385" height="366"]]

Given a pentagon of side 1 unit, show that the circle diameters are approximately 0.50952 units. || Hidetoshi and Rothman, 2008,Sacred Mathematics: Japanese Temple Geometry, pg 94 ||
 * [[image:isosceles_triangle.png width="474" height="363"]]

A circle of radius //r// is inscribed in an isosceles triangle with sides //a// = 12 and //b// = 10. Find //r//.

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How is the area of the inscribed circle related to the measure of the vertex angle?

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Here is a derivation of a formula that describes the relationship