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Geometry Level 3

To circles with center O , C O,C are drawn with radius 5 , 3 5,3 respectively such that they intersects at points A , B A,B and A B ‾ \overline{AB} becomes the diameter of the smaller circle as shown in the figure.

Find the a r e a o f t h e s h a d e d r e g i o n . \red{area\space of \space the \space shaded\space region}.

Bonus : Do it for general circles with radius r 1 , r 2 r_1,r_2 and A B ‾ = d \overline{AB}=d

Inspiration


The answer is 10.049.

Zakir Husain by Zakir Husain , 41, India

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1 solution

Saya Suka
Apr 19, 2021

Answer
= Small semicircle area + isosceles triangle area – Big circle's sector
= π(3²)/2 + (1/2)(3+3)√(5²–3²) – π(5²)(2×arcsin{3/5} / 360°)
= 10.049 unit²


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