Question

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

Answer 1

Answer:

Therefore the value of x is 25.8 unit.

Step-by-step 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

$(AB)^{2}=BC\times BD$

Substituting we get

$(y)^{2}=7\times 22=154\\\\Square\ Rooting\ we\ get\\\\y=\sqrt{154}=12.4\ unit\\\therefore AB = y = 12.4$

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

$(AB)^{2}=BE\times BF$

Substituting we get

$(12.4)^{2}=5\times (5+x)\\\\153.76=25+5x\\\\5x=128.76\\\\\therefore x=\dfrac{128.76}{5}=25.752\\\\\therefore x=25.8\ unit$

Therefore the value of x is 25.8 unit.