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  4. A circle is circumscribed about the triangle with sides, 8, 15, and 17 in such a manner that it divided the circle into 4 regions. Supposing X, Y, Z be the area of non-triangle regions with Z be the largest, then among the given choices, choose the correct option

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Q. A circle is circumscribed about the triangle with sides, 8, 15, and 17 in such a manner that it divided the circle into 4 regions. Supposing $X, Y, Z$ be the area of non-triangle regions with $Z$ be the largest, then among the given choices, choose the correct option

Mensuration

Solution:

Here we observe that the sum of the square of two sides of a triangle is equal to the square of third side that is
$8^2+15^2=17^2$
$\Rightarrow$ the given triangle is a right triangle.
If a circle circumscribed about the right triangle then hypotenuse is equal to diameter of a circle.
image
$\text { Area of triangle }=\frac{1}{2} \times 8 \times 15=60 $
$ \Rightarrow Z=X+Y=60$