Inscribed Tri & Rect - Angles

[mmslf75]

A rectangle inscribed in a circle necessarliy will have the center same as that of the circle ??

Whenever it is said that a triangle is inscribed in a circle, does it mean that the longest side of the trinagle rests on the diameter ??

[BuckeyeT]

That's a little vague. Do you have the exact question?

As far as inscribing a triangle in a circle, that only means that the points of the triangle lie on the circle (allowing all the lines of the triangle to be within the circle). It does NOT mean that the longest side of the triangle rests on the diameter. But IF a side of the triangle rests on the diameter of the circle, it IS the longest side of the triangle.

Try drawing it out. It's helpful

[mmslf75]

800 Score question

Rectangle PQST, with dimensions w × h, is inscribed in a circle with a radius of 1. Triangle QRS is isosceles with QR = RS and is inscribed in the circle as shown above. If triangle QRS and rectangle PQST have the same area, then what is the length of h?

A. 1/4
B. 2/5
C. 1/3
D. 1/2
E. 2/3


Query :

Does this mean that rectangle's center and circle's center coincide ?

Does this mean that triangle rests with longest side as DIAMETER of the circle ?