Inscribed Triangle

gmattesttaker2 wrote:Hello,

This is from P. 92 of MGMAT Geometry Strategy Guide:

Triangle ABC is inscribed in a circle. If the length of side AB is 6, the length of side AC is 8 and BC is a diameter of the circle, what is the area of the circle.

Ans: 25 pi

Now, the explanation gives the following diagram: (12_img.png)

I was wondering why the following diagram is in-correct in which I have BC passing through the center of the circle.(13_img.png)

niketdoshi123 wrote:

gmattesttaker2 wrote:Hello,

This is from P. 92 of MGMAT Geometry Strategy Guide:

Triangle ABC is inscribed in a circle. If the length of side AB is 6, the length of side AC is 8 and BC is a diameter of the circle, what is the area of the circle.

Ans: 25 pi

Now, the explanation gives the following diagram: (12_img.png)

I was wondering why the following diagram is in-correct in which I have BC passing through the center of the circle.(13_img.png)

Both the diagrams are correct.
The property that the question is testing is Inscribed Angle property.

Inscribed Angle Definition : the angle subtended at a point on the circle by two given points on the circle.

The diameter of the circle ,here BC, subtends 90° at any other point on the the circle, here A.
So, in this question the triangle ABC is 3-4-5 right angle triangle.