Thread: true statement

R, S, and T are points with RT=2RS. Which of the following could be true?

i. R, S, and T are the vertices of a right triangle
ii. R, S, and T are three of the vertices of a square.
iii. R, S, and T all lie on the circumference of a circle.


And I thank you all in advance

Originally Posted by Judi

R, S, and T are points with RT=2RS. Which of the following could be true?

i. R, S, and T are the vertices of a right triangle
ii. R, S, and T are three of the vertices of a square.
iii. R, S, and T all lie on the circumference of a circle.


And I thank you all in advance

i. If R, S and T were the vertices of a 30, 60, 90 triangle with proper
arrangement of the labels RT=2RS would be true.

ii. If this were the case RS would have to be a side of the square, and
RT the diagonal, but then 2RS^2 != RT^2, a contradiction

iii. A circle can be drawn through any three points in the plane.

RonL