Solution

The best way to solve this question is its evaluation upfront..

More often than not people start to calculate the arcs and then make the difference between the circle area and the triangle area.

Instead if you figure out that the figure DO NOT drwan the scale and that could be in this way



\(OR\)



You do not have inough information to come up with a solution

So the answer is \(D\)
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Actually, the source states also that the diameter of the circle is 10. I think it makes it a little bit trickier

Question corrected as per source.
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First of all, it's important not to read too much into the diagram.
All we can glean from the diagram is that we have a quadrilateral that is inscribed in the circle.
That's it!

So, first recognize that the inscribed quadrilateral COULD be a very very very narrow rectangle like this.

Notice that this quadrilateral COULD be so thin that its area is very very close to zero.
So, for this particular quadrilateral we get:
Quantity A: a very very small area that's close to zero
Quantity B: 40
In this case, Quantity B is greater.


Alternatively, we COULD make the quadrilateral quite large.
In fact, we could make it a SQUARE.


So, if the inscribed quadrilateral is a square, what is its area?
To find out, let's draw a diagonal.

One of our circle properties tells us that this diagonal must be the diameter of the circle, which we know is 10
To find the area of the square, we need to know the length of each side.
So, let's let x = the length of each side.

Since ACD is a RIGHT TRIANGLE, we can apply the Pythagorean Theorem to get: x² + x² = 10²
Simplify to get 2x² = 100
Divide both sides by 2 to get: x² = 50

This means the area of the square = 50
We know this because the area of the square = (x)(x) = x², and we just learned that x² = 50

So, for this particular quadrilateral we get:
Quantity A: 50
Quantity B: 40
In this case, Quantity A is greater.

Answer: D

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why do we need to change the shape? cant we calculate the values as per the given diagram?
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What values are you referring to?
All we're told is that the diameter of the circle is 10.
Other than the fact that the quadrilateral is inscribed in the circle, there's no other information that will "lock in" the area of the quadrilateral.
As such, we need to consider various possible scenarios.

Cheers,
Brent
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