HOW TO DO THIS? PLEASE HELP

Question

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Part 1

A right triangle has vertices​ X(0,0), Y(0,2a),​ Z(2b,0). What is the circumcenter of the​ triangle? Make a conjecture about the diameter of a circle that is circumscribed about a right triangle.

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Part 1

The circumcenter is at --------

​(Type an ordered​ pair.)

Part 2

What conjecture can you make about the diameter of a circle that is circumscribed about a right​ triangle?

A.

ΔABC

is a right​ angle, and the circumcenter lies at the midpoint of the shortest leg. So the length of the shortest leg is equal to the length of the diameter of the circumscribed circle.

B.

ΔABC

is a right​ angle, and the circumcenter is at the same location of the incenter. This means that the radius is equal to the perpendicular bisector of the right​ angle, so the diameter is twice the length of the perpendicular bisector of the right angle.

C.

ΔABC

is a right​ angle, and the circumcenter lies at the midpoint of the longest leg. So the length of the longest leg is equal to the length of the diameter of the circumscribed circle.

D.

ΔABC

is a right​ angle, and the circumcenter lies at the midpoint of the hypotenuse. So the length of the hypotenuse is equal to the length of the diameter of the circumscribed circle.

Answer 1

You need to think about this problem yourself and ask specific questions in places where you get stuck.

Draw a figure.

Draw the perpendicular bisectors of the legs which will meet at the midpoint of the hypotenuse. Do you know why this must be the circumcenter?

There is a geometry theorem often called the Side-splitter Theorem which answers this question and you should know about that theorem (and if you don't, please ask).

Part D requires you to know that an angle inscribed in a semi-circle is a right angle...and again if you do not know why this is so, please ask.

Answer 2

Hi,

I got this question very late.

It is a right triangle. The hypotenuse is a diameter of the circle that contains the vertexes of the triangle.

Then, the midpoint of the hypotenuse is the center.

There is no triangle ABC. There is triangle XYZ. The right angle is at the origin, where is point X.

The right answer is D.