If a right angled triangle is inscribed in a circle, is it necessary for the hypotenuse of the right triangle to be the diameter of the circle? I know that the vice-versa is true.
You can figure this out by drawing a diagram.
Ques3.jpg [ 9.44 KiB | Viewed 9217 times ]
Look how the angle is increasing as you go higher up. Hence for every length of the minor arc, there is a unique inscribed and central angle. The right triangle's hypotenuse will be the largest length of the chord i.e. a diameter and its central angle will be 180 giving the inscribed angle as 90.
Also, length of arc = (Central angle/360) * 2*pi*r
Since inscribed angle is 90, central angle is 180.
length of arc = 180/360 * (2*pi*r)
length of arc = pi*r
i.e. you get a semi circle. So the chord (the hypotenuse of the right triangle) must be the diameter.
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