Question

what is rs?
rs =
submit
work it out
not feeling ready yet? these can help
tangent lines (10)
additive prope
perimeter
lesson: tangen

Explanation:

Step1: Use the property of tangents to a circle in a quadrilateral

If a quadrilateral is circumscribed about a circle (a tangential quadrilateral), then the sum of the lengths of two opposite sides is equal to the sum of the lengths of the other two opposite sides. So, \(OQ + MS=OM + QS\). Also, for a tangential quadrilateral, if we consider the tangent - segment lengths: \(OQ = OP\), \(QP=QR\), \(RS = ST\), \(MT=MN\), \(NO = NP\).
We know that \(OQ = 29\), \(QR = 9\). Let \(RS=x\) and \(MS = 34\), \(OM=34\).
Since \(OQ + MS=OM + QS\) and \(QS=QR + RS\)
Substitute the values into the equation: \(29+34 = 34+(9 + x)\)

Step2: Solve the equation for \(x\)

Simplify the left - hand side of the equation: \(29+34=63\)
Simplify the right - hand side of the equation: \(34+(9 + x)=43 + x\)
Then we have the equation \(63=43 + x\)
Subtract 43 from both sides: \(x=63 - 43\)

Answer:

\(20\)