Question

what is the length of line segment pq? 4 units 5 units 6 units 9 units

Explanation:

Step1: Apply secant - secant rule

If two secants are drawn to a circle from an exterior point, then the product of the lengths of one secant segment and its external segment is equal to the product of the lengths of the other secant segment and its external segment. Let the length of $PQ=x$. We have $(x + 4)\times4=6\times(6 + 4)$.

Step2: Expand the equation

$4x+16 = 60$.

Step3: Solve for $x$

Subtract 16 from both sides: $4x=60 - 16=44$. Then divide both sides by 4: $x = 6$.

Answer:

B. 6 units