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

Question

https://gmatclub.com/forum/download/file.php?id=43317 What is the area of the triangle PQR in the circle shown above? (1) ac = 100 (2) bc = 5\sqrt{100} image010.jpg

ravikumarmishra · Answer

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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bbegumbayar · Answer

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

PKN · Answer

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)

swim2109 · Answer

Bunuel  can you put the official answer explanation.

ZodiacZ · Answer

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

swim2109 · Answer

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

bumpbot · Answer

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

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

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