Answer:
4.5
Step-by-step explanation:
First things first - the triangle OCB is similar to ODB - because they are symmetrically reflected over OB. They are also both right triangles, because the tangent is perpendicular to the corresponding radius.
BD = BC
We also know that (because it's a right triangle):
[tex]OB = \sqrt{OC^2 + BC^2}\\\\5.3 = \sqrt{2.8^2 + BC^2}\\\\5.3^2 = 2.8^2 + BC^2\\\\BC = \sqrt{5.3^2 - 2.8^2} = \sqrt{28.09 - 7.84}= \sqrt{20.25} = 4.5\\\\BD = BC = 4.5[/tex]
