Centre of Circles

Geometry Level 3

Three circles of radii 1,2 and 3 units respectively touch each other externally in the plane. What is the circumradius of the triangle formed by joining the centers of the three circles?


The answer is 2.5.

Mishal Sheik by Mishal Sheik , 19, India

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1 solution

The triangle in question has side lengths 1 + 2 = 3 , 1 + 3 = 4 1 + 2 = 3, 1 + 3 = 4 and 2 + 3 = 5 2 + 3 = 5 , and is thus a right triangle. The circumradius of a right triangle is one half the length of the hypotenuse, and so in this case is 1 2 × 5 = 2.5 \dfrac{1}{2} \times 5 = \boxed{2.5} .

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I feel that the problem would benefit from a new image, one that does not have all three circles with apparently the same radius.

Marta Reece - 4 years ago

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