Question 126

Each of the two circles of same radius a passes through the centre of the other; If the circles cut each other at the points A and Band 0, 0′ be their centres, area of the quadrilateral AOBO’ is :

Solution

Let the radius of each circle be $$a$$

In $$\triangle$$ OAO'

=> OO' = OA = O'A = $$a$$

=> $$\triangle$$OAO' is equilateral triangle.

Similarly, $$\triangle$$OBO' is equilateral triangle

=> ar(AOBO') = $$\triangle$$OAO' + $$\triangle$$OBO'

= $$2 * \frac{\sqrt{3}}{4} a^2$$

= $$\frac{\sqrt{3}}{2} a^2$$

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