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# Triangle inscribed in a semicircle

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Manager
Joined: 06 Jan 2008
Posts: 215
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Triangle inscribed in a semicircle [#permalink]  02 May 2008, 17:48
Can someone explain to me why a triangle inscribed in a semicircle is always a right triangle? I understand it is isosceles because of the radii, but what makes it always a right triangle?
Senior Manager
Joined: 20 Feb 2008
Posts: 296
Location: Bangalore, India
Schools: R1:Cornell, Yale, NYU. R2: Haas, MIT, Ross
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Re: Triangle inscribed in a semicircle [#permalink]  02 May 2008, 19:53
Hi,

This is my interpretation. If you consider a semicircle, the central angle is 180 degrees.

And we know that an inscribed angle is half the central angle so :

The triangle whose angle is 90 is 1/2 the central angle which is 180.I am not sure why this is the case exactly but my guess is that the central angle is a factor of r and an angle inscribed on the circle is a factor of the diameter = 2r and therefore the angle will decrease by a factor of 1/2.

Hope this helps!
Director
Joined: 01 Jan 2008
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Re: Triangle inscribed in a semicircle [#permalink]  03 May 2008, 01:06
Good question,

Ventivish response is correct .

Theorem: An angle inscribed in a Semi-circle is a right angle.
http://www.algebra.com/algebra/homework ... cle.lesson
Re: Triangle inscribed in a semicircle   [#permalink] 03 May 2008, 01:06
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