Question

How length of /AC/ = ?

Answer 1

`AC=16` cm

Explanation:

As two tangent segments to a circle from an external point are equal in length, `=> CD=CT=8`,
`=> BC=BD-CD=12-8=4`,
As `CT` is tangent to circle centered at `O_1`, and `CBA` is the secant line, by tangent-secant theorem, we get:
`CT^2=CA*CB`
`=> 8^2=CAxx4`,
`=> AC=64/4=16` cm

Proof of tangent-secant theorem is available in the link below:
https://socratic.org/questions/let-m-be-a-point-and-c-a-circle-m-doesn-t-belong-to-the-c-let-a-and-b-be-points-#471096