turkey-yks 2019 Q38

turkey-yks · Other · yks-ayt Circles Area and Geometric Measurement Involving Circles
In a plane, three circles with radius r are constructed with the vertices of a right triangle $ABC$ as centers, and these circles do not intersect each other. The lengths of the parts on the sides of the triangle that are not inside these circles are given as 2 units, 3 units, and 5 units. Accordingly, what is the total area of the regions inside the circles but outside the triangle in square units?
A) $6 \pi$
B) $8 \pi$
C) $9 \pi$
D) $\frac { 9 \pi } { 2 }$
E) $\frac { 15 \pi } { 2 }$
In a plane, three circles with radius r are constructed with the vertices of a right triangle $ABC$ as centers, and these circles do not intersect each other. The lengths of the parts on the sides of the triangle that are not inside these circles are given as 2 units, 3 units, and 5 units.\\
Accordingly, what is the total area of the regions inside the circles but outside the triangle in square units?\\
A) $6 \pi$\\
B) $8 \pi$\\
C) $9 \pi$\\
D) $\frac { 9 \pi } { 2 }$\\
E) $\frac { 15 \pi } { 2 }$