Responses/hints: PUZZLE #73 Circles inside triangles

 

A.  Here is a hint: if you connect the vertices A, B, C to the center of the circle D you get 3 triangles with height r. The sum of the areas of these 3 triangles must of course equal the area of the given isosceles triangle.

      

       OK, so we have rAB/2 + rBC/2 + rAC/2 = 2(4x3/2),

(did you notice that the perendicular AD splits ABC into a pair of 3,4,5 triangles?)

       So we have r5/2 + r6/2 + r5/2= 12, which is equivalent to r = 3/2.

 

B. The circle has area pi.r2= 7.07approx., and the triangle has area 12, so twice the area of the circle is larger.

 

 

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