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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.
We can use the substitution method to solve this problem.
The second equation is
, so we can plug in 2x for 'y' in the first equation:
Multiply:
Combine like terms:
This is the x-value of our solution, we can plug this into any of the two equations to find the y-value:
Multiply:
This is the y-value of our solution. So our entire solution is (3, 6).
The second equation is
Multiply:
Combine like terms:
This is the x-value of our solution, we can plug this into any of the two equations to find the y-value:
Multiply:
This is the y-value of our solution. So our entire solution is (3, 6).