Question

the figure below shows a circle with center p and diameter overline{jc}. which of the angles must be right angles? select all that apply.

Explanation:

Step1: Recall Thales' theorem

Thales' theorem states that an angle inscribed in a semicircle is a right - angle.

Step2: Identify the semicircle and inscribed angles

Since \(JC\) is the diameter of the circle, the arc \(JVC\) and arc \(JBC\) are semicircles.
For an inscribed angle, the angle whose vertex is on the circle and whose sides contain the endpoints of the diameter.
The angle \(\angle JBC\) is inscribed in the semicircle \(JBC\) (because the endpoints of the diameter \(JC\) and the vertex \(B\) is on the circle).
The angle \(\angle JVC\) is inscribed in the semicircle \(JVC\) (because the endpoints of the diameter \(JC\) and the vertex \(V\) is on the circle).

Answer:

\(\angle JBC\) and \(\angle JVC\)