Question

Secant RM intersects secant RN at point R. Find the length of RQ. If necessary, round to the hundredths place.

Answer 1

Answer:

3 Units

Step-by-step explanation:

Secant RM intersects secant RN at point R.

The secants intersects the circle at points P and Q respectively as seen in the diagram.

To determine the length of RQ, we use the Theorem of Intersecting Secants.

Applying this on the diagram, we have:

RP x RN=RQ X RM

4(4+5)=RQ(RQ+9)

Let the length of RQ=x

$4*9=x^2+9x\\36=x^2+9x\\x^2+9x-36=0\\x^2+12x-3x-36=0\\x(x+12)-3(x+12)=0\\(x+12)(x-3)=0\\x+12=0 x-3=0\\x=-12 or x=3\\Since x cannot be negative \\x=|RQ|=3$

Therefore, length of RQ=3 Units