Question 1199742
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The radii OE and OF are perpendicular to the sides of the kite, so triangles AFO and OEC are both similar to triangle ADC.<br>
Let r be the radius of the circle; let x be the length of segment FD.<br>
In similar triangles AFO and ADC, AF/FO = AD/DC:<br>
{{{(24-x)/r=24/18=4/3}}}
{{{4r=72-3x}}}
{{{3x+4r=72}}} [1]<br>
In similar triangles OEC and ADC, EC/OE = DC/AD:<br>
{{{(18-x)/r=18/24=3/4}}}
{{{3r=72-4x}}}
{{{4x+3r=72}}} [2]<br>
Solve [1] and [2] for r by eliminating x.<br>
{{{12x+16r=288}}}
{{{12x+9r=216}}}
{{{7r=72}}}
{{{r=72/7}}}<br>
ANSWER: 72/7 = 10 2/7 = D<br>