Question

the figure below shows a circle with center o, diameter ds, secants dc and dx, and tangent cw. which of the angles must be right angles? select all that apply. answer ∠cdx ∠dnc ∠dcn ∠doc ∠odc ∠ocn

Explanation:

Step1: Recall tangent - radius property

A tangent to a circle is perpendicular to the radius at the point of tangency. So, $\angle OCN = 90^{\circ}$ since $CW$ is tangent to the circle with center $O$ at point $C$ and $OC$ is the radius.

Step2: Analyze other angles

There is no information or geometric property that would make $\angle CDX$, $\angle DNC$, $\angle DCN$, $\angle DOC$, $\angle ODC$ right - angles. $\angle CDX$ is formed by two secants, $\angle DNC$ is an interior angle of a non - right triangle formed by the secants, $\angle DCN$ is an angle in a non - right triangle, $\angle DOC$ is a central angle, and $\angle ODC$ is an angle in $\triangle DOC$ which is not a right triangle in general.

Answer:

$\angle OCN$