Maybe you can do President Garfield's proof and combine it with a history lesson.
page 161 of the New-England Journal of Education, April 1, 1876 (image from Google Books)
Note: M. C. = Member of Congress.
This was in my math folder, I don't know its source.
It was shown as 'not needing any further explanation', but of course, for lower level students, I connect the 3 points on the circle's perimeter to form the larger right triangle and remind them of the ratios formed by dropping an altitude (line b).