Inscribed angles

[JulianMathHelp]

The definition of an inscribed angle is an angle created by two chords intersecting, and the vertex is on the circumfrence.

In a semi-circle, there's a theorem where an inscribed angle is always 90 degrees, however, isn't this not always true? It is only true if the inscribed angle's chords contain the endpoints of the diameter.

 

[pka]

The definition of an inscribed angle is an angle created by two chords intersecting, and the vertex is on the circumfrence.
In a semi-circle, there's a theorem where an inscribed angle is always 90 degrees, however, isn't this not always true? It is only true if the inscribed angle's chords contain the endpoints of the diameter.

First some vocabulary. The circumference is a number. The circle is the circle. The theorem is: If two cords join opposite ends of a diameter of a circle to a point on the circle then the angle formed is a right angle, measure \(\left(\dfrac{\pi}{2}\right)\).
Definition: an inscribed angle is formed be two cords that intersect at a point on the circle.

 

[JulianMathHelp]

Ok

First some vocabulary. The circumference is a number. The circle is the circle. The theorem is: If two cords join opposite ends of a diameter of a circle to a point on the circle then the angle formed is a right angle, measure \(\left(\dfrac{\pi}{2}\right)\).
Definition: an inscribed angle is formed be two cords that intersect at a point on the circle.

Ok, so my theorem was wrong,

 

[pka]

Ok, so my theorem was wrong,

Are you quoting from a college level axiomatic geometry text book? If so please tell us which.
Would you also quote the theorem ti which you are referring?

 

[JulianMathHelp]

Are you quoting from a college level axiomatic geometry text book? If so please tell us which.
Would you also quote the theorem ti which you are referring?

I am quoting from a website. "Any angle inscribed in a semi-circle is a right angle." The website I got the quote from is: http://www.geom.uiuc.edu/~dwiggins/conj44.html

Also looked at this one: https://www.mathopenref.com/semiinscribed.html

 

[lev888]

I am quoting from a website. "Any angle inscribed in a semi-circle is a right angle." The website I got the quote from is: http://www.geom.uiuc.edu/~dwiggins/conj44.html

Also looked at this one: https://www.mathopenref.com/semiinscribed.html

"inscribed in a semicircle" probably means "inscribed angle's chords contain the endpoints of the diameter".

 

[JulianMathHelp]

"inscribed in a semicircle" probably means "inscribed angle's chords contain the endpoints of the diameter".

That's must be true as it is the only way it makes sense.