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## #1 2013-07-09 12:06:47

romani
Member
Registered: 2013-06-28
Posts: 3

### 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:

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## #2 2013-07-10 00:23:41

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,706

### 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

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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