How Great It Is?

Geometry Level 4

State the length of the radius to the nearest integer.

Coordinates of the vertices are; (500, 250), (747, 845), (254, 842), and (188, 748).


The answer is 348.

Guiseppi Butel by Guiseppi Butel , 90, Canada

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1 solution

Saurav Pal
Feb 28, 2015

By using the coordinates of the bigger triangle I found out the sides of that triangle i.e 641.0772184, 644.2313249 and 493.0091277. The area of this triangle comes out to be 146297. The radius of the circumcircle can be calculated by using the formula R = a b c 4 Δ R= \frac {abc}{4\Delta} , which comes to be 347.9459054. Hence, the integer nearest to this number is 348 \boxed { 348 } .

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