Answer:
Part 7) [tex]AB=27\ units[/tex]
Part 8) [tex]x=1.7\ units[/tex]
Step-by-step explanation:
Part 7) Find the length of AB
we know that
The two tangent theorem states that if we draw two lines from the same point which lies outside a circle, such that both lines are tangent to the circle, then their lengths are the same
so
In this problem, applying the two tangent theorem
AB=BC
substitute the given values
[tex]15x-3=10x+7[/tex]
solve for x
[tex]15x-10x=7+3\\5x=10\\x=2[/tex]
Find the length of AB
[tex]AB=15x-3[/tex]
substitute the value of x
[tex]AB=15(2)-3=27\ units[/tex]
Part 8) we know that
If CD is tangent to circle E at point C
then
Line segment CD is perpendicular to line segment EC (radius) and CDE is a right triangle
so
Applying the Pythagorean Theorem in the right triangle CDE
[tex]DE^2=CD^2+EC^2[/tex]
substitute the given values
[tex]2^2=x^2+1^2[/tex]
solve for x
[tex]4=x^2+1\\x^2=3\\x=1.7\ units[/tex]
