if a triangle has side legths 6 8 and 10, if a circle is drawn through its vertices , what is the diameter of the circle?
I see that the triangle is a pythagoren triple, but im having trouble explaining it
2007-01-13 05:34:59 · 5 answers · asked by brennen 1 in Science & Mathematics ➔ Mathematics
The diameter is 10, because the length of the hypotenuse is 10. Here's why:
Recall that the diameter of any circle is also a chord of the same circle. But this particular chord passes through the center of the circle, which means it cuts the circle into two equal arcs of 180 degrees. Recall also that the measure of any inscribed angle of a circle is half the measure of the central angle which subtends the same arc of the circle. One of the vertices of this triangle is a right angle, 90 degrees, which means it subtends an arc equal to twice its measure when measured from the center of the circle (central angle). This means that the measure of the arc which it subtends is 2 x 90 = 180 degrees. The only central angle which has this measure is the arc subtended by the endpoints of the diameter. Therefore, the side opposite the 90 degree angle, which must have length equal to 10 units given the figures here and by the Pythagorean Theorem, and which also satisfies the special properties of inscribed right angles is the diameter. So, the diameter is 10 units long.
2007-01-13 06:33:42 · answer #1 · answered by MathBioMajor 7 · 0⤊ 0⤋
The diameter of the circle is 10... The triangle is right-angled, that is, the sum of the squares of the two shorter sides is equal to the square of the longest side. A triangle inscribed in a semicircle is a right triangle.
2007-01-13 05:52:20 · answer #2 · answered by john l 2 · 0⤊ 0⤋
Diameter of Circle = 10
There is a theorem:
If you draw a triangle inside a semicircle, the angle opposite the diameter is 90°.
Thus by the above theorem , the diameter will be 10.Since the angle opposite to this side is 90 degree.
For more info on this theorem:
http://www.egge.net/~savory/maths18.htm
2007-01-13 06:46:16 · answer #3 · answered by @rrsu 4 · 0⤊ 0⤋
The diameter of the circle is 10.
If you have an inscribed right triangle inside of a circle where the points form a right triangle, the hypotenuse is the diameter.
more info on here
http://en.wikipedia.org/wiki/Thales%27_theorem
2007-01-13 06:30:24 · answer #4 · answered by OSO 3 · 0⤊ 0⤋
dont know but thanks for the 2 points
2007-01-13 05:42:58 · answer #5 · answered by koolkoree@sbcglobal.net 1 · 0⤊ 0⤋