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A quadrilateral with sides 15, 15, 15 and 20 is drawn with each vertex on a circle. Around this circle, a square is drawn, with each side tangent to the circle. What is the area, in square units, of this square?

Someone suggested to me to use vectors, but I haven't learnt them yet. Is there another way to answer this question?

uservg
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    What is your attempt? Presumably you are doing contest math questions to challenge yourself. If so, you need to make a good effort to solve the problem yourself before asking for help. If you cannot even start then read up on Cyclic Quadrilaterals. – sammy gerbil Apr 27 '20 at 14:24

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This is equivalent to finding $4r^2$, where $r$ is the circumradius of the cyclic quadrilateral.

There are many ways to find $r$. One way is by letting one of the angle be $\theta$. Then the opposite angle will be $180-\theta$. Then use cosine rule and equate $\cos(\theta)=-\cos(180-\theta)$.

Another way is to simply use this.

Gareth Ma
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