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
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:
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:
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