# Thread: Oh No, It's A Trapezoid

1. ## Oh No, It's A Trapezoid

In the diagram, a circle (trust me) is inscribed in an isosceles trapezoid whose parallel sides have lengths 8 and 18, as indicated. What is the diameter of the circle?

2. ## Re: Oh No, It's A Trapezoid

<span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow>13?</font color=yellow></span hi>

3. ## Re: Oh No, It's A Trapezoid

<span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow>The diameter is 12</font color=yellow></span hi>

<span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow>The distance of the upper vertices to the points of intersection is 8/2 = 4; for the lower vertices, it is 18/2 = 9. So the non-parallel sides have lengths 4+9 = 13. A perpendicular line from an upper vertex to the bottom intersects the bottom at a distance of (18-8)/2 = 5 from the nearest lower vertex. Pythagoras tells us that the length of the perpendicular line is 12 (it's in a 5-12-13 triangle)</font color=yellow></span hi>

4. ## Re: Oh No, It's A Trapezoid

A+ <img src=/S/bullseye.gif border=0 alt=bullseye width=45 height=15>

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