If a triangle inscribed in a semicircle has area 40, what is the area

HiShruti0805 ,

Why st1 is insufficient is already explained.

Refer red-highlightes line in your post. It's incorrect, rather st2 says one of the angle of the triabgle is 30 degree.

You know, any diameter of a circle subtends a right angle to any point on the circle.
Now we know two angles of the triangle( 90 and 30 degree) , so th emeasure of the third side is 180-90-30=60 degree
Hence the triangle is in the form 30-60-90.

Hope it's clear.

HiShruti0805 ,

Why st1 is insufficient is already explained.

Refer red-highlightes line in your post. It's incorrect, rather st2 says one of the angle of the triabgle is 30 degree.

You know, any diameter of a circle subtends a right angle to any point on the circle.
Now we know two angles of the triangle( 90 and 30 degree) , so th emeasure of the third side is 180-90-30=60 degree
Hence the triangle is in the form 30-60-90.

Hope it's clear.[/quote]Hi,

Statement 2 doesn't really mention that the entire diameter is being used as a side. We could use just a smaller part of the diameter as a side and form a triangle that doesn't have its 3rd vertex on the edge of the circle, right? That creates a triangle which isn't a right triangle and makes this statement insufficient.

Sent from my A0001 using GMAT Club Forum mobile app

Hi,

What do we mean by the term INSCRIBED?
it usually means drawing one shape inside another so that it just touches.

HERE THE TRIANGLE IS INSCRIBED IN THE SEMI-CIRCLE, which implies that the vertices of the triangle touch the circumference of the semi-circle and two extreme points of the diameter. If you consider smaller portion of the diameter as the sides of the triangle then we can't call the resultant figure as an inscribed triangle in a semi-circle.

A sample figure is enclosed.

Solution

Given:

• A triangle, which is inscribed in a semicircle, has area of 40 sq. units

To find:

• Area of the circle

Analysing Statement 1
“One side of the triangle is equal to the diameter of the circle”

• Implies, it is a right-angled triangle
• And, the hypotenuse of the triangle is the diameter of the circle
• However, we cannot find the diameter, as we do not have any information about the other sides of the triangle.

Therefore, Statement 1 is NOT sufficient to arrive at a unique answer

Analysing Statement 2
“The measure of one of the angles is 30”

• The other angles of the triangle can be anything, such that their sum = 180 – 30 = 150
• However, we cannot infer anything else from this information

Therefore, Statement 2 is NOT sufficient to arrive at a unique answer

Combining Both Statements
• From Statement 1, we know that, one of the angles of triangle = 90, and the diameter of the circle is the hypotenuse of the triangle

• From Statement 2, we know that one of the angles of triangle = 30
• Combining both, we get, the angles of the triangle as 30. 60 and 90
• Now, let’s assume the diameter as D

o The other two sides of the triangle will be, DSin30 and DCos30 = D/2 and √3D/2
o Thus, area of the triangle = 1/2 * D/2 * √3D/2 = 40
• From this we get a unique value of D, so, we get a unique value for the area of the circle.

Therefore, both statements TOGETHER are sufficient to arrive at a unique answer.

Hence, the correct answer is option C.

Answer: C

Bunuel & EgmatQuantExpert:

OA provided by Bunuel is different from the Answer derived by EgmatQuantExpert.

Can we have a consensus on this, plz?

good catch I am also looking for clarification

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