1993 UNCO Math Contest II Problems/Problem 9

Problem

Let $P$ be a point inside the rectangle $ABCD$ . If $AP=5$ , $BP=11$ and $CP=10$ , find the length of $DP$ . (Hint: draw helpful vertical and horizontal lines.)

$[asy] pair P=(2,2); draw((0,0)--(0,5)--(10,5)--(10,0)--cycle,dot); draw((0,0)--P,black); draw((0,5)--P,black); draw((10,5)--P,black); draw((10,0)--P,black); dot(P); MP("P",(1,1),N); MP("5",(1.5,2.9),N); MP("10",(6.5,2.8),N); MP("11",(6.5,.9),N); MP("A",(0,5),NW); MP("B",(10,5),NE); MP("C",(10,0),SE); MP("D",(0,0),SW); [/asy]$

Solution

By the British Flag Theorem, we have $AP^2$ + $CP^2$ = $BP^2$ + $DP^2$ . Substituting in, we have 25+121=100+ $DP^2$ . We find $DP$ to be $\sqrt{46}$ .

1993 UNCO Math Contest II (Problems • Answer Key • Resources)
Preceded by Problem 8	Followed by Problem 10
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10
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1993 UNCO Math Contest II Problems/Problem 9

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