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A triangle with sides of length 36 cm, 77 cm, and 85 cm are inscribed in a circle.
Inside the triangle a second circle is inscribed. What is the area in square centimetres,
between the two circles?
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Notice that the given triangle is a right-angled triangle, since
36^2 + 77^2 = 7225 = 85^2.
Since this triangle is inscribed to the larger circle, its hypotenuse is the DIAMETER of the larger circle.
Thus the larger circle's diameter is 85 cm; hence, the larger circle's radius is R = 85/2 = 42.5 cm.
Next, the radius of the inscribed circle is (as for any right angled triangle)
r = = = 14 cm
where "a" and "b" are the legs, 36 cm and 77 cm, while "c" is the hypotenuse 85 cm.
Now the area between the circles is
= = = = 5058.745 cm^2. ANSWER
Solved.