Question

Find the value x please help me I’m so confused

Answer 1

Therefore the value of x is 25.8 unit.

Explanation:

Given:

AB =Tangent = y

BE = secant segment = 5

BC = secant segment = 7

EF = x

CD = 15

To Find :

x = ?

Solution:

Tangent-secant theorem:

"When a tangent and a secant are drawn from one single external point to a circle, square of the length of tangent segment must be equal to the product of lengths of whole secant segment and the exterior portion of secant segment."

Here we have

AB =Tangent

BC = secant segment = 7

BD = exterior portion of secant segment = BC +CD =7 + 15 = 22

So on applying Tangent-secant theorem we get

`(AB)^(2)=BC* BD`

Substituting we get

`(y)^(2)=7* 22=154\\\\Square\ Rooting\ we\ get\\\\y=√(154)=12.4\ unit\\\therefore AB = y = 12.4`

Now again applying Tangent-secant theorem for different secant we get

`(AB)^(2)=BE* BF`

Substituting we get

`(12.4)^(2)=5* (5+x)\\\\153.76=25+5x\\\\5x=128.76\\\\\therefore x=(128.76)/(5)=25.752\\\\\therefore x=25.8\ unit`

Therefore the value of x is 25.8 unit.