Question

the figure below shows a circle with center a, diameter (overline{ip}), and tangents (overleftrightarrow{sl},overleftrightarrow{pl}), and (overleftrightarrow{ic}). which of the angles must be right angles? select all that apply.

Explanation:

Step1: Recall the property of tangent to a circle

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

Step2: Analyze each tangent - radius pair

• For tangent \(\overleftrightarrow{SL}\) and radius \(AS\): Since \(\overleftrightarrow{SL}\) is a tangent and \(AS\) is the radius, \(\angle ASL = 90^{\circ}\) (by the tangent - radius property).
• For tangent \(\overleftrightarrow{PL}\) and radius \(AP\): Since \(\overleftrightarrow{PL}\) is a tangent and \(AP\) is the radius, \(\angle APL=90^{\circ}\) (by the tangent - radius property).
• For tangent \(\overleftrightarrow{IC}\) and radius \(AI\): Since \(\overleftrightarrow{IC}\) is a tangent and \(AI\) is the radius, \(\angle AIC = 90^{\circ}\) (by the tangent - radius property).

Answer:

\(\angle ASL\), \(\angle APL\), \(\angle AIC\)