What is the required area?

Geometry Level 2

A triangle with side lengths 16, 18, and 21 has a circle with radius 6 centered at each vertex. What is the total area inside the three circles but outside of the triangle is equal to (the yellow part)?

30 π 30\pi 60 π 60\pi 36 π 36\pi 12 π 12\pi 90 π 90\pi

Hana Wehbi by Hana Wehbi , 51, USA

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1 solution

Marta Reece
Jul 26, 2018

There are three circles radius 6. From that 1 2 \frac12 of a circle is subtracted (as the angles inside a triangle have to add up to 18 0 ∘ 180^\circ ).

So the area is 2.5 × 6 2 × π = 90 π 2.5\times 6^2\times \pi=\boxed{90\pi} .

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Don't you mean 2.5, not 3.5?

Samir Betmouni - 2 years, 10 months ago

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Yes, of course. Thank you.

Marta Reece - 2 years, 10 months ago

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