Given:
Tangent segment MN = 6
External segment NQ = 4
Secant segment NP =x + 4
To find:
The length of line segment PQ.
Solution:
Property of tangent and secant segment:
If a secant and a tangent intersect outside a circle, then the product of the secant segment and external segment is equal to the product of the tangent segment.
[tex]\Rightarrow NQ\times NP = MN^2[/tex]
[tex]\Rightarrow 4\times (x+4) = 6^2[/tex]
[tex]\Rightarrow 4x+16 = 36[/tex]
Subtract 16 from both sides.
[tex]\Rightarrow 4x+16-16 = 36-16[/tex]
[tex]\Rightarrow 4x =20[/tex]
Divide by 4 on both sides.
[tex]$\Rightarrow\frac{4x}{4}=\frac{20}{4}[/tex]
[tex]\Rightarrow x = 5[/tex]
The length of line segment PQ is 5 units.
