Question

1. two circles have the same center o. the radius of the larger circle is twice the radius of the smaller circle.

select all of the following that are congruent to the radius of the smaller circle.
$overline{xo}$
$overline{yd}$
$overline{dc}$
$overline{co}$
$overline{oa}$
$overline{dx}$
$overline{oy}$
$overline{db}$

Explanation:

Step1: Define radii variables

Let the radius of the smaller circle be $r$. Then the radius of the larger circle is $2r$.

Step2: Identify smaller circle radii

Radii of the smaller circle: $\overline{XO}$, $\overline{OY}$, $\overline{CO}$. All equal to $r$, so they are congruent to each other.

Step3: Identify lengths equal to $r$

• $\overline{DX}$: Radius of larger circle ($2r$) minus radius of smaller circle ($r$), so $\overline{DX}=2r - r = r$.
• $\overline{YD}$: Same as $\overline{DX}$, $\overline{YD}=2r - r = r$.
• $\overline{DC}$: $\overline{DO}=2r$, $\overline{CO}=r$, so $\overline{DC}=2r - r = r$.
• $\overline{OA}=2r$ (larger radius, not equal to $r$), $\overline{DB}=2r$ (chord, not equal to $r$).

Answer:

$\overline{XO}$, $\overline{OY}$, $\overline{CO}$, $\overline{YD}$, $\overline{DX}$, $\overline{DC}$