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

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Math Expert
Joined: 02 Sep 2009
Posts: 53060
What is the area of the triangle PQR in the circle shown above?  [#permalink]

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05 Sep 2018, 22:40
00:00

Difficulty:

45% (medium)

Question Stats:

62% (02:02) correct 38% (02:04) wrong based on 36 sessions

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

(1) ac = 100

(2) $$bc = 5\sqrt{100}$$

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Re: What is the area of the triangle PQR in the circle shown above?  [#permalink]

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05 Sep 2018, 23:30
1
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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What is the area of the triangle PQR in the circle shown above?  [#permalink]

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06 Sep 2018, 01:21
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
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Re: What is the area of the triangle PQR in the circle shown above?  [#permalink]

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07 Sep 2018, 01:46
bbegumbayar wrote:
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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Re: What is the area of the triangle PQR in the circle shown above?   [#permalink] 07 Sep 2018, 01:46
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