Inscribed Triangle

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Sat Aug 11, 2012 9:53 pm

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)

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Source: Beat The GMAT — Problem Solving | Sat Aug 11, 2012 9:53 pm

niketdoshi123: Master | Next Rank: 500 Posts; Posts: 210; Joined: Thu Mar 08, 2012 11:24 pmFollowed by: 3 members; Thanked: 62 times

by niketdoshi123 » Sat Aug 11, 2012 11:09 pm

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

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Sun Aug 12, 2012 7:38 pm

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

Hello Niket,

Thank you very much for the explanation. It is clear now.

Best Regards,
Sri

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