Question

the figure below shows a circle with center z, diameter $overline{bk}$, secants $overleftrightarrow{bv}$ and $overleftrightarrow{by}$, and tangent $overleftrightarrow{va}$. which of the angles must be right angles? select all that apply.

Explanation:

Step1: Recall circle - tangent property

A tangent to a circle is perpendicular to the radius at the point of tangency. Here, $\overrightarrow{VA}$ is tangent to the circle at point $V$ and $ZV$ is the radius. So, $\angle ZVA = 90^{\circ}$.

Step2: Recall semi - circle angle property

An angle inscribed in a semi - circle is a right angle. Since $\overline{BK}$ is a diameter, the angle subtended by the diameter at any point on the circle (such as $\angle BVK$) is a right angle.

Answer:

$\angle ZVA$, $\angle BVK$