Question

what is uv?
uv =
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work it out
not feeling ready yet? these can help:
tangent lines (10)
additive property

Explanation:

Step1: Use the property of tangents from a common external point

For a polygon circumscribed about a circle (a tangential polygon), the lengths of the two tangent segments drawn from an external point to a circle are equal.
Let's assume the lengths of the tangent segments: \(TS = TZ\), \(UZ=UY\), \(VX = VW\), \(WX = WY\)
The perimeter formula for a quadrilateral \(TUVZ\) circumscribed about a circle: \(P = 2(TS + UV+ WX)\) (or \(P=2(TU + VX)\))
We know that \(TS = TZ = 20 - 13=7\) (This is wrong, actually, for a tangential quadrilateral \(TUVX\) (assuming the correct vertices), the sum of the lengths of opposite sides are equal.
The property of a tangential quadrilateral: \(TU + VX=UV + TZ\)
We know that \(TU = 13\), \(TZ = 20 - ( \text{length from }T\text{ to the point of tangency on }TU)\), but the correct property is \(TU+VX = UV + TZ\)
Another way: In a tangential quadrilateral, \(TU + VX=UV + TZ\)
We are given \(TU = 13\), \(VX=18\), \(TZ = 15\)

Step2: Solve for \(UV\)

By the formula \(TU + VX=UV + TZ\)
Substitute the values: \(13 + 18=UV + 15\)
Rearrange the equation: \(UV=13 + 18- 15\)
Calculate \(13+18 = 31\), then \(31-15=16\)

Answer:

\(16\)