Triangle QSR is inscribed in a semi-cirlce is QSR a right triangle?

A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s hypotenuse, then that triangle is a right triangle.(1) QR is a diameter of the circle --> according to the above property QSR must be a right triangle. Sufficient.

(2) Length QS equals 3 and length QR equals to 5 --> it's not necessary QSR to be 3-4-5 right triangle (therefor QR to be diameter/hypotenuse), for example if diameter is more than 5, say 10 than it's possible to inscribe QSR in a semi-circle so that SR would be the largest side and QSR would be obtuse-angled triangle. Not sufficient. (Would help if you just try to draw it).

Answer: A.

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