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sleet_krkn [62]
2 years ago
8

HELP PLEASE BE QUICK

Mathematics
1 answer:
natka813 [3]2 years ago
6 0

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<u><em> two tangent theorem</em></u> 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

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