In the figure below, the segments BC and BD are tangent to the circle centered at O. Given that =OC2.8 and =OB5.3, find BD

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):

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)

i think da answer is

d.square root of 3