Question

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

Answer 1

4.5

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):

`OB = √(OC^2 + BC^2)\\\\5.3 = √(2.8^2 + BC^2)\\\\5.3^2 = 2.8^2 + BC^2\\\\BC = √(5.3^2 - 2.8^2) = √(28.09 - 7.84)= √(20.25) = 4.5\\\\BD = BC = 4.5`