This question is wrong! Don't worry, your two solutions are right!

Proving that this problem is wrong is as follows, which requires high school knowledge. You can choose to continue reading:

∠BCF=∠FAD

So cosBCF=3/4, sinBCF=√5/4.

According to cosine theorem

BF？ = (BC? +CF？ )-2bc * cfcosbcf =16+100/9-2 * 4 *10/3 * 3/4 = > BF = 8/3 (except negative values).

According to sine theorem

CF/sinB=BF/sinBCF

sinB = CF sin BCF/BF = 10/3 *√5/4 * 3/8 = 5√5/ 16≦√3/2

So ∠B≠60 degrees

So ∠B+∠BAC≠90 degrees.

AB is by no means a diameter ⊙ o.

This is in contradiction with this topic.

So, this question is wrong! If the exam questions are wrong or ambiguous, once found, both scores need to be judged correctly! (Refer to this year's comprehensive disputes ~)