Problem:
Points A and C lie on a circle centered at O, each of BA and BC are tangent to the circle, and △ABC is equilateral. The circle intersects BO at D. What is BOBD​?
Answer Choices:
A. 32​​
B. 21​
C. 33​​
D. 22​​
E. 23​​
Solution:
Let the radius of the circle be r. Because △BCO is a right triangle with a 30∘ angle at B, the hypotenuse BO is twice as long as OC, so BO=2r. It follows that BD=2r−r=r, and
