Question

the figure below shows a circle with center v, diameter \\( \overline{qa} \\), and tangents \\( \overleftrightarrow{xc} \\) and \\( \overleftrightarrow{ar} \\). which of the angles must be right angles? select all that apply.

Explanation:

Step1: Recall the tangent - radius theorem

A tangent to a circle is perpendicular to the radius at the point of tangency.

Step2: Identify the right - angled triangles

Since \(\overleftrightarrow{XC}\) is a tangent and \(VX\) is a radius, \(\angle VXC = 90^{\circ}\).
Since \(\overleftrightarrow{AR}\) is a tangent and \(VA\) is a radius, \(\angle VAR=90^{\circ}\).

Answer:

\(\angle VXC\) and \(\angle VAR\)