In circle o, bc =19 and dc=35. the diagram is not to scale.
what is the length of diameter ba? .

1. CD is tangent to the circle with center O, at point D. 

2. Join D to O. 

3. OD = OB = r, where r is the radius of the circle. 

4. radius OD is perpendicular to the tangent CD.

5. Thus in the right triangle OCD: , by the pythagorean theorem.

6.



Note: when applying pythagorean theorem, the difference of squares property
[  ] is a useful practical tool in calculations.

38r=(35 -19)(35+19)
38r=16*54

r=

7. Finally, the diameter BA=2r=2*22.74=45.48

So the answer is 45.5