Question

NO LINKS. Find the segment length indicated. Assume that lines which appear to be tangent are tangent. PLEASE SHOW WORK!!​

Answer 1

? = 9.2

Explanation:

The angle between a tangent and radius at the point of contact is 90°

Then the triangle shown is right with legs ? , 6.9 and hypotenuse = (6.9 + 4.2) = 11.5

Using Pythagoras' identity in the right triangle

?² + 6.9² = 11.5²

?² + 47.61 = 132.25 ( subtract 47.61 from both sides )

?² = 84.64 ( take the square root of both sides )

? =
`√(84.64)` = 9.2

Answer 2

Solution given:

BC=BD=6.9 units

AD=4.6units

Now

AB=4.6+6.9=11.5units.

we have

<C=90°[the line from the tangent is perpendicular to the radius of circle]

we know that ∆ABC is a right angled triangle.

hypotenuse [h]=AB=11.5units

base[b]=BC=6.9 units

perpendicular [p]=x units

By using Pythagoras law

h²=p² +b²

11.5²=x²+6.9²

x²=11.5²-6.9²

x²=84.64

x=
`√(86.64)`=9.2

Sothe segment length indicated is 9.2 units.