Question

AD is tangent to circle O at D. Find AB. Round to the nearest tenth if necessary. Thank you.

Answer 1

AB=2.1

Explanation:

we know that

Applying the Intersecting Secant-Tangent Theorem

`(BC+AB)(AB)=AD^(2)`

substitute the given values and solve for AB

`(15+AB)(AB)=6^(2)`

Let

x=AB

substitute

`(15+x)(x)=36`

`x^(2)+15x-36=0`

Solve the quadratic equation by graphing

The solution is x=2.1

see the attached figure

therefore

AB=2.1