Question

HELP PLEASE BE QUICK

Answer 1

Answer:

Part 7) $AB=27\ units$

Part 8) $x=1.7\ units$

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

$15x-3=10x+7$

solve for x

$15x-10x=7+3\\5x=10\\x=2$

Find the length of AB

$AB=15x-3$

substitute the value of x

$AB=15(2)-3=27\ units$

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

$DE^2=CD^2+EC^2$

substitute the given values

$2^2=x^2+1^2$

solve for x

$4=x^2+1\\x^2=3\\x=1.7\ units$