Answer:
x = 26
Step-by-step explanation:
Given
(x - 2) =
(x + 4) + 2
Multiply through by 15 to clear the fractions
5(x - 2) =3(x + 4) + 30 ← distribute and simplify both sides
5x - 10 = 3x + 12 + 30, that is
5x - 10 = 3x + 42 ( subtract 3x from both sides )
2x - 10 = 42 ( add 10 to both sides )
2x = 52 ( divide both sides by 2 )
x = 26
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.
Subtract 16 from both sides.
Divide by 4 on both sides.
The length of line segment PQ is 5 units.