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Triangle inscribed within a circle...

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Triangle inscribed within a circle...

by pkw209 » Thu Feb 25, 2010 2:50 pm
For a triangle inscribed within a circle (and all points of the triangle touching the circle's circumference), if one side of the triangle is the diameter is it always assumed to be the hypotenuse?

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by papgust » Thu Feb 25, 2010 5:40 pm
Yes. Because, a triangle with one side as a diameter forms a right-angle (90 degrees) opposite to the side that is a diameter. A side opposite to a right-angle is a hypotenuse. So, that side is a hypotenuse.
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by kstv » Thu Feb 25, 2010 9:50 pm
Another way of looking at it is

an angle BAC whose vertex A lies on a circle is said to be inscribed into the circle . The arc BC subtends an angle at the centre which will be twice BAC. But if BC is the diameter through the centre O , hypothetically angle BOC is 180°. So BAC is 90°.
check the link

https://www.cut-the-knot.org/Curriculum/ ... ngle.shtml
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