If a right triangle is inscribed in a circle, is the hypotenuse of circle always the diameter ?
Can anyone verify / prove it ?
MAdhur
Can anyone verify / prove it ?
MAdhur
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Right Triangle inscribed in a circle
Source: Beat The GMAT — Problem Solving |
jus a little proof:
lets assume that the hypotenuse in not always the diameter and we will later contradict this.
see the image
let line CD is the hypotenuse and angle COD=90
let AB is the diameter, so we know that angle AOB is 90
as you can see
both the angles AOB and angle COD can be equal only when AB=CD
so that contradicts our assumption.
May be not the exact prrof u were looking for, but still..
lets assume that the hypotenuse in not always the diameter and we will later contradict this.
see the image
let line CD is the hypotenuse and angle COD=90
let AB is the diameter, so we know that angle AOB is 90
as you can see
both the angles AOB and angle COD can be equal only when AB=CD
so that contradicts our assumption.
May be not the exact prrof u were looking for, but still..
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The powers of two are bloody impolite!!
Thanks a lot.
Can anyone point me to some resource summarizing such theorems. Especially related to cicrumscribed and inscribed circles.
Madhur
Can anyone point me to some resource summarizing such theorems. Especially related to cicrumscribed and inscribed circles.
Madhur
