Question

what is ip?
19
l
k
m
18
j
12
n
i
o
24
p
ip =
submit

Explanation:

Step1: Use the property of tangents to a circle

For a quadrilateral circumscribed about a circle (a tangential quadrilateral), the sum of the lengths of two opposite sides is equal to the sum of the lengths of the other two opposite sides. That is \(JK + NP=JL + MP\). Also, if we consider the tangent - segment property: if two tangent segments are drawn from an external point to a circle, then the lengths of the two tangent segments are equal. So \(JI = JK\), \(LI = LM\), \(MN=NO\), \(PO = PI\).

We know that \(JK + NP=JL + MP\). Let \(IP=x\).

We have \(JK = 19\), \(NP = 24\), \(JL=18\), \(MP = 12 + x\)

Step2: Set up the equation

Substitute the values into the equation \(JK + NP=JL + MP\)

$$19+24=18+(12 + x)$$

$$43=30 + x$$

$$x=43 - 30$$

$$x = 13$$

Answer:

\(13\)