Question

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

• A. $Z-X=Y+50$
• B. $Z=X+Y+60$
• C. $X+Y=Z$
• D. $Z-X=Y$

Answer 1

Answer: (B)

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.

$\text{ Area of triangle }=\frac{1}{2}\times 8\times 15=60$
$\Rightarrow Z=X+Y=60$