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Hi TSS Graviser,
First of all, thank you so much for pointing out the error in the images! We will fix it as soon as possible. As a note, although the images are different, you should still be able to solve the problem, since the angle of arc AB is given.
For your second question "What if the chord is directly across the circle?", I'm assuming you mean if the chord goes across the circle through its diameter; please correct me if I misunderstood. If the chord passes through the diameter, the angle between the tangent and the chord would be 90°, because the tangent is perpendicular to the radius that touches it.
For your last question, you can refer to the Module 2 Week 2 Day 6 Your Turn Explanation video starting around 5:38, where Prof. Loh explains the \( \frac{a+b}{2} \) formula.
I hope this helps!
Happy Learning,
The Daily Challenge Team