Knowledge Check
Question 17
A circle with center $H$ is shown in the figure below.
(a) Name a radius:
(b) Name a diameter:
(c) Name a chord:
(d) If the length of $\overline{H G}$ is 2 units, what is the length of $\overline{I J}$ ?
Megan
E
Answer
(d) Since the length of \(\overline{HG}\) is 2 units and \(\overline{HG}\) is a radius of the circle, the length of \(\overline{IJ}\), which is a diameter of the circle, is twice the length of the radius. Therefore, the length of \(\overline{IJ}\) is \(\boxed{4}\) units.
Step 1 ：(a) A radius of the circle could be \(\overline{HG}\), \(\overline{HI}\), or \(\overline{HJ}\).
Step 2 ：(b) A diameter of the circle could be \(\overline{GJ}\), \(\overline{GI}\), or \(\overline{IJ}\).
Step 3 ：(c) A chord of the circle could be \(\overline{GJ}\), \(\overline{GI}\), or \(\overline{IJ}\).
Step 4 ：(d) Since the length of \(\overline{HG}\) is 2 units and \(\overline{HG}\) is a radius of the circle, the length of \(\overline{IJ}\), which is a diameter of the circle, is twice the length of the radius. Therefore, the length of \(\overline{IJ}\) is \(\boxed{4}\) units.
