(QK) is also equal to 22.
To find (QK), use the property that in a right triangle, the diameter of the circumscribed circle is twice the length of the hypotenuse.
Given (XY = 32) and (XZ = 30), are the legs of the right triangle (XYZ).
The hypotenuse, (YZ), can be found using the Pythagorean Theorem:
YZ = √(XY² + XZ²)
YZ = √(32² + 30²)
YZ = √1024 + 900
YZ = √1924
YZ ≈ 44
The radius of the circumscribed circle is half the hypotenuse:
R = YZ / 2
R = 44 / 2
R = 22
So, the radius of the circumscribed circle is 22.
To find (QK), use the fact that (QK) is a radius of the circumscribed circle.
i.e QK = R
If R = 22, QK = 22
Therefore, (QK) is also equal to 22.