Given:
Secant segment = 14 in and 10 in
Length of tangent = x in
To find:
Length of tangent x.
Solution:
Secant segment = 14 in
External segment = 10 + 14
= 24 in
Tangent- secant theorem:
If a secant and a tangent intersect outside a circle, then the product of the secant segment and external segment is equal to the square of the tangent segment.
[tex]\Rightarrow x^2 = 24\times 10[/tex]
[tex]\Rightarrow x^2 = 240[/tex]
Taking square root on both sides.
[tex]\Rightarrow x = 4\sqrt{15}[/tex]
[tex]\Rightarrow x = 15.5[/tex]
The length of the tangent segment is 15.5 in.
