Difference between revisions of "1993 UNCO Math Contest II Problems/Problem 9"
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== Problem == | == Problem == | ||
− | Let <math>P</math> be a point inside the rectangle <math>ABCD</math>. If <math>AP=5</math> , <math>BP= | + | Let <math>P</math> be a point inside the rectangle <math>ABCD</math>. If <math>AP=5</math> , <math>BP=10</math> and <math>CP=11</math>, find the length of <math>DP</math>. |
(Hint: draw helpful vertical and horizontal lines.) | (Hint: draw helpful vertical and horizontal lines.) | ||
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== Solution == | == 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}. | + | By the [[British Flag Theorem]], we have <math>AP^2+CP^2</math>=<math>BP^2+DP^2</math>. Substituting in, we have <math>25+121=100+DP^2</math>. We find <math>DP</math> to be <math>\boxed{\sqrt{46}}</math>. |
== See also == | == See also == |
Latest revision as of 01:07, 20 January 2023
Problem
Let be a point inside the rectangle
. If
,
and
, find the length of
.
(Hint: draw helpful vertical and horizontal lines.)
Solution
By the British Flag Theorem, we have =
. Substituting in, we have
. We find
to be
.
See also
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 | ||
All UNCO Math Contest Problems and Solutions |