Question

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

Answer 1

Answer:

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

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

Step-by-step 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

$x^{2} =11.4^{2}+(7.6+7.6)^{2}\\ \\ x^{2}=129.96+231.04\\ \\x^{2}=361\\ \\x=19\ units$