What is the area of the triangle PQR in the circle shown above?

using both equations you can cancel out c and get the ratio of a AND b. so we cannot find exact values of a, b and c, hence insufficient. it should be E.


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Is the point btw P and R the origin of the circle? Can we know it without explanation?

If it is the origin, we also know that a.c=b^2

Property of right angled triangle:-
If the altitude is drawn to the hypotenuse of a right triangle, each leg of the right triangle is the geometric mean of the hypotenuse and the segment of the hypotenuse adjacent to the leg.
Hence, \(b^2=a*c\)------(a)

The point between P and R is not the center of the circle.

Question stem:- Area of triangle PQR?
Or, \(\frac{1}{2} (a+c)*b=?\)
For this, we must know the unique values of a,b, and c.

St1:- ac = 100
Or, \(b^2=ac=100\)
Or, b=10
But notice that a and c have more than one value, such as (a=25,c=4), (a=50, c=2)
So, the value of area is not unique.
Insufficient.

st2:- \(bc=5\sqrt{100}=50\)
Value of 'a' is unknown.
Insufficient.

Combined, b=10, ac=100,and bc=50
So, we have c=5, a=20.
Hence, area can be determined.
Sufficient.

Ans. (C)
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Bunuel can you put the official answer explanation.

It is nowhere given that 'a+c' is the diameter of the circle. Hence the answer should be E.

How is b^2=ac? Bunuel please put up the official answer of this

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