Question

the figure below shows a circle with center x, diameter (overline{lg}), and secant (overleftrightarrow{ls}). which of the angles must be right angles? select all that apply.

Explanation:

Step1: Recall the Thales' theorem

Thales' theorem states that an angle inscribed in a semicircle is a right - angle. In a circle, if we have a diameter \(LG\) (so the arc \(LG\) is a semicircle), then for any point \(P\) on the circle (other than \(L\) and \(G\)), the angle \(\angle LPG\) is a right - angle.

Step2: Identify the angles

For the given circle with center \(X\) and diameter \(LG\):

• For the quadrilateral \(TLEG\) inscribed in the circle, \(\angle T\) and \(\angle E\) subtend the semicircle \(LG\).

Answer:

\(\angle T\) and \(\angle E\)