Figure 5.57: The diagram shows chords HS and JT passing through the center O. Given m(arc HT) = m(arc JH) and m( ∠PTH) = 58°, find m( arc HT).

Here are the solutions for Question 2 from the image.

Question 2: Figure 5.57

The problem statement contains contradictory information. The diagram shows chords HS and JT passing through the center O, which implies they are diameters. If they are diameters, then $m(\text{arc HT}) + m(\text{arc JH}) = 180^\circ$. However, the problem also states $m(\text{arc HT}) = m(\text{arc JH})$. These two conditions can only be simultaneously true if $m(\text{arc HT}) = m(\text{arc JH}) = 90^\circ$. But, using the given $m(\angle PTH) = 58^\circ$ and the Tangent-Chord Theorem, we find