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
[tex](AB)^{2}=BC\times BD[/tex]
Substituting we get
[tex](y)^{2}=7\times 22=154\\\\Square\ Rooting\ we\ get\\\\y=\sqrt{154}=12.4\ unit\\\therefore AB = y = 12.4[/tex]
Now again applying Tangent-secant theorem for different secant we get
[tex](AB)^{2}=BE\times BF[/tex]
Substituting we get
[tex](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[/tex]
Therefore the value of x is 25.8 unit.
