Question

What is the length of line segment PQ? If you can please explain, thanks.

Answer 1

Answer:

PQ=5

Step-by-step explanation:

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Answer 2

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.

$\Rightarrow NQ\times NP = MN^2$

$\Rightarrow 4\times (x+4) = 6^2$

$\Rightarrow 4x+16 = 36$

Subtract 16 from both sides.

$\Rightarrow 4x+16-16 = 36-16$

$\Rightarrow 4x =20$

Divide by 4 on both sides.

$\Rightarrow\frac{4x}{4}=\frac{20}{4}$

$\Rightarrow x = 5$

The length of line segment PQ is 5 units.