TITLE: The area of the region bounded by three mutually-tangent circles
QUESTION [6 upvotes]: Here 3 circles are touching each other.
Now how can one find the area of the blue shaded region in the given picture?

REPLY [8 votes]: Hints have been given in the comments. To make it more complete, I add a few more.

(1) $AB = R_1 + R_2$, and similar results for $BC$ and $CA$.
(2) Because all sides of $\triangle ABC$ are known, all three angles (in radians) can be found by applying cosine law (three times) (or cosine law then sine law and then " angle sum of triangle").
(3) Need to apply the conversion ratio ($\pi$ radian $= 180$ degrees) if not already done so in (2).
(4) Area of the yellow sector $= \frac {1}{2}(R_2)^2 \theta $. Again, $\theta$ should be in radian.
(5) Area of $\triangle ABC$ can be found by Heron’s formula or by the area formula $A = \frac {1}{2}ab. \sin C$.