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## #1 2013-07-10 10:06:47

romani
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### Triangle inscribed in a semicircle

Okay, so I've found this geometry question that's making me crazy (because I'm really weak in geometry, sighs)
Could you help me? c:
The question is as it follows:

take the segment AB with a lenght 6. Consider a semicircle with AB as the diameter. Let P be a point on the arc AB. Let x = <ABP.
1) express the area of the triangle ABP in terms of X.
2) find the range of x for which the are of the triangle

3) if the point P is so chosen that PA + PB =
holds, find the area of the triangle ABP.

I don't know how to find the area in terms of X, but with this area found, I think I can manage the other questions.
Thank you c:

## #2 2013-07-10 22:23:41

bob bundy
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### Re: Triangle inscribed in a semicircle

hi romani

There's a theorem in geometry that says that if A, B and P are points on the circumference with O as the centre then angle AOB = 2 x angle APB.

So if AOB is a diameter then AOB = 180 =>  APB = 90

So now you can use sines and cosines to get the base and height of the triangle and hence the area.

angle properties of a circle:

http://www.mathisfunforum.com/viewtopic.php?id=17799

Bob