Question

Find the segment length indicated. Assume that lines which appear to be tangent are tangent.

Answer 1

Part 1) The segment length indicated is
`6.4\ units`

Part 2) The segment length indicated is
`19\ units`

Explanation:

Let

x------> the segment length indicated

Part 1)

Applying the Pythagoras Theorem

`(13+x)^(2)=13^(2)+14.4^(2)\\ \\ (169+26x+x^(2))=169+207.36\\ \\x^(2)+26x-207.36=0`

Solve the quadratic equation by graphing

The solution is
`x=6.4\ units`

see the attached figure N 1

Part 2)

Applying the Pythagoras Theorem

`x^(2) =11.4^(2)+(7.6+7.6)^(2)\\ \\ x^(2)=129.96+231.04\\ \\x^(2)=361\\ \\x=19\ units`